相关论文: Jacobian Elliptic Wave Solutions for the Wadati-Se…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
In this manuscript, consideration is given to the existence of periodic traveling-wave solutions to the $abcd$-system. This system was derived by Bona, Saut, and Chen to describe small amplitude, long wavelength gravity waves on the surface…
Some systems were recently put forth by Nguyen et. al. as models for studying the interaction of long and short waves in dispersive media. These systems were shown to possess synchronized Jacobi elliptic solutions as well as synchronized…
A new algebraic method to find two special types of exact traveling wave solutions and the solitary type solutions to some conformable fractional partial differential equations is proposed. The two special types of solutions given by the…
The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear…
New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
We give a detailed study of the traveling wave solutions of $(\ell=2)$ Kaup-Boussinesq type of coupled KdV equations. Depending upon the zeros of a fourth degree polynomial, we have cases where there exist no nontrivial real solutions,…
The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi's functions are obtained for the nonlinear Schr\"{o}dinger equation governing the propagation of pulses in optical fibers including the effects of…
Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the $\mathrm{tanh}$-method. The method works by…
We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
In this article, we investigate monotonicity of limit wave speed of periodic traveling wave solutions for a perturbed generalized KdV equation via Abelian integral. We have answered an open problem outlined by Yan et al. (2014) and the…
We introduce the concept of soliton solutions of integrable nonlinear partial differential equations and point out that the inverse spectral method represents the rigorous mathematical formalism to construct such solutions. We work with the…
The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows…
Exact bright, dark, antikink solitary waves and Jacobi elliptic function solutions of the generalized Benjamin-Bona-Mahony equation with arbitrary power-law nonlinearity will be constructed in this work. The method used to carry out the…
In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic…
In order to find analytically the travelling waves of partially integrable autonomous nonlinear partial differential equations, many methods have been proposed over the ages: "projective Riccati method", "tanh-method", "exponential method",…
We apply the version of the method of simplest equation called modified method of simplest equation for obtaining exact traveling wave solutions of a class of equations that contain as particular case a nonlinear PDE that models shallow…