Keywords plasma, variational theory, burger equation, semiinverse method. The included perturbation terms are all of hamiltonian type. Using some illustrative examples, it was shown that the semi inverse variational method is a powerful and straightforward solution method to find closedform for schrodingertype equations. Kuramotosivashinsky equation, variational principle, semiinverse method. A detailed derivation is elucidated step by step by the semi inverse method, and some special cases are discussed. It is most frequently used to compute the ground state, but can be extended to compute the low lying excited states. Variational method to solve moving boundary problem 230 thermal science, year 2011, vol. The partial differential equation of fitzhughnagumo is modified by the appropriate wave transforms into a dimensionless nonlinear ordinary differential equation, which is solved by a semi inverse variational method. Variationalformulation according to hes variational method 8 for soli. This paper secures exact bright, dark and singular soliton solutions with parabolicnonlocal combo nonlinearity in polarizationpreserving optical fibers. Moreover, we study in detail the numerical analysis and the numerical implementation.
Recently, two significant variational methods are proposed by he. The significance of variable separation is confirmed once more. Approximation methods in quantum mechanics science. The semi inverse method is used to establish variational principles directly from the. Pdf hes semiinverse method for camassaholm equation. On the basis of the variational principle obtained, a solitary solution is obtained, which is the same as debnaths result l.
Therefore, the method of semi inverse variational principle svp is implemented to reveal an analytical expression for bright 1soliton solution. The semi inverse method is proposed by he to establish the generalized variational principles for physical problems, which can eliminate variational crisis brought by the lagrange multiplier method. Variational principle for a generalized kdv equation in a. Several methods have been used to solve fractional differential equations such as. Application of hes variational iteration method to solve. Application of hes expfunction method and semi inverse variational principle to equal width wave ew and modified equal width wave mew equations h.
Variational principles for some nonlinear wave equations. A note on the semiinverse method and a variational principle. Exact solutions of the equation of one dimensional motion. The process is schematically described in figure 1. Jul 01, 2009 using some illustrative examples, it was shown that the semi inverse variational method is a powerful and straightforward solution method to find closedform for schrodingertype equations. According to the semi inverse method 23, we write a lagrangian in the form.
Variational principle for traveling waves in a modified kuramoto. Numerical modeling for generating the bound state energy via. The established variational formulation suggests an energy conservation for the fractal nonlinear oscillator, and its. Application of hes expfunction method and semi inverse. A variational method in image recovery siam journal on. Probabilistic representation and inverse design of.
Variational approach to foam drainage equation springerlink. Journal of low frequency noise, confusion threshold study. Research interest pdevariational methods for image processing. Homotopy perturbation method hpm1 and variational iteration method vim2. In order to use the semi inverse method to establish a lagrangianfor, we rst check some simple cases. Semiinverse method and generalized variational principles with. A modified lihes variational principle for plasma emerald. Abstractthis paper studies optical solitons, in presence of higher order dispersion terms by the aid of hes semi inverse variational principle. Variational principle for nonlinear oscillator arising in a. Inverse problems, variational regularization on riemannian manifolds, functions of bounded variation 1 introduction. Crosskink wave solutions and semiinverse variational method. We established variational formulations for the coupled nonlinear kleingordon zakharov equations by hes semiinverse method. Optical solitons with quadraticcubic nonlinearity by semi.
Subsequently, an analytical bright 1soliton solution is recovered, in the presence of higherorder dispersion effects by semi inverse variational principle. Crosskink wave solutions and semiinverse variational. Pdf generalized variational principle for long water. He, 2006, which is now widely applied in fractional calculus baleanu et al. The semi inverse variational principle is employed in order to obtain an analytical soliton solution in presence of the perturbation terms. In this part, we will illustrate how to establish a variational principle for a nonlinear problem using the semi inverse method. This note reveals that the semi inverse method also works for a generalized kdvmkdv equation with nonlinear terms of any orders. They are typically used in complex statistical models consisting of observed variables usually termed data as well as unknown parameters and latent variables, with various sorts of relationships among the three types of random variables, as.
By semi inverse method, the author has also proved that huwashizu principle is actually a variational principle with only two kinds of independent variables, stressstrain relations are still its constraints. Eulerlagrange equation by variational method 46, 15. Nov 27, 2020 variational principles for ginzburglandau equation by hes semi inverse method chaos solitons fractals, 33 5 2007, pp. Variational principles for multiwalled carbon nanotubes undergoing nonlinear vibrations by semi inverse method. Building blocks for spatial problems week 47 o optimal interpolation method stationary and nonstationary covariance models covariance calibration using maximumlikelihood o 3d variational method tangent linear jacobian and adjoint models of nonlinear observation forward model. We apply the semi inverse method to search for its variational principle. By semi inverse method, the author has also proved that huwashizu principle is actually a variational principle with only two kinds of independent variables. It is concluded that the semi inverse method is a powerful tool for searching for variational principles directly from the governing equations. Journal of low frequency noise, a modified harmonic. Introduction solitary solution is a hot topics in nonlinear science.
Finally, we provide for three di erent inverse problems numerical experiments. Variational principle for nonlinear schrodinger equation with high. Pdf hes semiinverse method for camassaholm equation and. The semi inverse method is used to establish a variational principle for the dirichlet boundary value problem with impulses. Xu established a variational formulation for coupled. This method was successfully applied to solve initial. Generalized variational principle for electromagnetic. International journal of modern mathematical science. Variational principle for a generalized kdv equation. This implies the need for inversion of a nonlinear operator gp with p denoting the parameters to compute, but allows to skip the process of generating noisy images. A generalized kdv equation with fractal derivatives is suggested, and a special function is introduced to establish a fractal variational principle. Recently, variational and hamiltonian principles are two interesting approaches to solve strong nonlinear problems. Asen 6055 data assimilation and inverse methods for earth and. Pdf variational approach to impulsive differential.
Variational principles for bending and vibration of partially. Optical soliton perturbation with parabolicnonlocal combo. Thus, this paper is thus going to address equation 1 on the most generalized setting so far, and the tool of integration is going to be the svp. The direct relationship between these two techniques is mathematically described. Journal of low frequency noise, a modified harmonic balance. From realistic examples, some state configurations are presented. Theoretical underpinnings and novel applications find. Variational approximations from the rayleighritz variational principle. All the boundary conditions can be obtained as natural conditions by. The semi inverse method suggested by the author is one of the best and most convenient ways to deduce generalized variational principles with multivariables from 1 partial differential equations.
Variational method is one of the popular approaches for inverse consistent deformable image registration. Exact eigenspectra and eigenfunctions of the dirac quantum equation are established using the semi inverse variational method. A variational approach for novel solitary solutions of. Variational theory for linear magnetoelectroelasticity. It can replace lagrange multiplication to establish the generalized variational principle. Zhang established a variational formulation of the generalized zakharov equation using the semi inverse method, and. Variational principle and periodic solution of the kundu. Application of hes semiinverse method to the nonlinear. The eulerlagrange equation with respect to u is eq. In this paper, we have shown a possible connection between the semi inverse variational method and the evaluation of solutions of a given quantum system.
A nonlinear variational method for improved quanti. A semiinverse variational method for generating the bound. Convergence of variational regularization methods for. Letter to the editor a note on the semiinverse method and a. Hes variational principle is a very dominant instrument to find the solitary solutions for various nonlinear equations. Variational formulations provide the basis for a number of approximate and numerical methods.
Semiinverse method and generalized variational principles. Feb 18, 2019 probabilistic representation and inverse design of metamaterials based on a deep generative model with semi supervised learning strategy wei ma, feng cheng, yihao xu, qinlong wen, and yongmin liu doi. Among them, variational approaches, such as he,s semi inverse method 10 is a powerful tool to the search. However, this optimization is nontrivial because the elbo is highly nonconvex and nonlinear. Equivalence of the existed two in literature is shown. The variational principle is a foundation of the variational iteration method anjum and he, 2019. The method of weighted residuals and variational principles. Using the semi inverse method, a variational principle is established, and the following solitary solution is obtained via the ritz method. The model performances are demonstrated for the coulomb type problem.
A note on the semi inverse method and a variational principle for the generalized kdvmkdv equation. Raslan 3,4 1department of mathematics, faculty of science, menoufia university, shebein elkoom, egypt. Pdf variational iteration method for solving nonlinear. Variational principle for traveling waves in a modified kuramotosivashinsky equation. A variational finite element method for source inversion for. Variational bayesian methods are a family of techniques for approximating intractable integrals arising in bayesian inference and machine learning. Letter to the editor a note on the semiinverse method and. Variational autoencoder for endtoend control of autonomous driving with novelty detection and training debiasing alexander amini 1, wilko schwarting, guy rosman2, brandon araki, sertac karaman3, daniela rus1 abstractthis paper introduces a new method for endtoend training of deep neural networks dnns and evaluates. Variational autoencoder for endtoend control of autonomous driving with novelty detection and training debiasing alexander amini 1, wilko schwarting, guy rosman2, brandon araki, sertac karaman3, daniela rus1 abstractthis paper introduces a new method for endto. Variational principles are established for the partially composite timoshenko beam using the semi inverse method. This note reveals that the semiinverse method also works for a generalized kdvmkdv equation with nonlinear terms of any orders. The semiinverse variational principle is employed in order to obtain an analytical soliton solution in presence of the perturbation terms.
Recently, two signi cant variational methods are proposed by he. Soliton solutions of the perturbed resonant nonlinear. In this work, a nonlinear oscillator model with a fractal derivative is successfully established for a fractal nanomicroelectromechanical system mems, and its variational principle is obtained by the semi. We use the semi inverse variational method together with bspline bases to extract the structures of bound states of the schrodinger equation. S229s239 he 24, 25 first proposed the variational iteration method vim to solve nonlinear differential and integral equations. From the given examples, we found that it is difficult to find a variational principle for nonlinear evolution equations with nonlinear terms of any orders. A note on the semiinverse method and a variational principle for. In 1, the semi inverse method is systematically studied and many examples are given to show how to establish a variational formulation for a nonlinear equation. By using the legendrefenchel transform, we show how the nonquadratic criterion to be minimized can be split into a sequence of halfquadratic problems easier to solve numerically. This paper is concerned with a classical denoising and deblurring problem in image recovery. In, the semi inverse method is systematically studied and many examples are given to show how to establish a variational formulation for a nonlinear equation. This research concerns with the development of a linear threedimensional numerical model in a quantum environment.
The vim is developed by employing a correction functional and general lagrange multiplayer for the differential equation, then by the variational principle the optimum value is obtained for the correction functional and it is solved using the iteration method 3. A semiinverse variational method for generating the bound state. Applications of hes variational principle method and. Xu succeed in establishing the needed variational principle forkm,n equations. Applications of hes variational principle method and modification of. V v 2 for v 0, v 2 2 for v 0, v3 6 for v2 2 v v 0, v 1 for v 2. Some applications for different state configurations are proposed to concretize the method. On the computation of the lagrange multiplier for the. The aim of this paper is to couple hes semi inverse method 14 and the expfunctionmethod 16 to search for solitary solutions of the discussed problem. Generalized variational principle for long waterwave. Optical soliton perturbation with kudryashovs equation by.
From the given examples, we found that it is di cult to nd a variational principle for nonlinear evolution equations with nonlinearterms of any orders. Ouyang, accelerated schemes for a class of variational inequalities, a special issue of stochastic equilibrium and variational inequalities in mathematical programming b submitted. Variational principles for bending and vibration of. Pdf on the semiinverse method and variational principle. Keywords variational theory, semi inverse method, solitary solution, expfunction method, jacobielliptic function 1. Comparison of lagrange multiplier for nonlinear bvps. Furthermore, he34 applied this method to solve some. Semi inverse method and variational principle are explained in this chapter, and the hamiltonian and variational approaches are discussed in detail.
We apply hes semi inverse method to establish a variational theory for the coupled nonlinear kleingordon zakharov equations. Chen, a fractionalorder derivative based variational framework for image denoising, inverse problem and imaging,to appear. A semiinverse variational method for generating the bound state energy eigenvalues in a quantum system. This method minimizes an energy functionals symmetric to the forward and backward transformations, and in general, consists of three parts. The pochhammerchreeequation consider the pochhammerchree equation governed by 23 u tt. New solitary wave solution for the boussinesq wave equation. A note on the semiinverse method and a variational. New solitary wave solution for the boussinesq wave.
Recently many new analytical methods were appeared to find solitary solutions of various nonlinear equations, such. Semi inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics. This method improves of a considerable manner the efficiency and accuracy of results compared with the other usual methods much argued in the literature. Numerical modeling for generating the bound state energy. From the given examples, we found that it is difficult to find a variational principle for nonlinear. Variational methods the variational technique represents a completely di. A model for an anisotropic flexoelectric material with cubic. Research article variational principles for bending and. Conclusionsin this letter, we have used hes variational method to search for solitary solutions. The semi inverse method is of great guiding importance to the theory of variation. The heat conduction equation is restudied by the semi inverse method combined with separation of variables.
Semi inverse method of establishing generalized principles for. The semi inverse method is a powerful tool to establish variational principles from the governing equations. Variational autoencoder for endtoend control of autonomous. In this paper we will illustrate how to establish a variational principle for a nonlinear problem using the semi inverse method. Convergence of variational regularization methods for imaging.
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