Related papers: Nonlinear wave solution to a coupled mKdV equation…
Quasi-periodic solutions with multiple base frequencies exhibit the feature of $2\pi$-periodicity with respect to each of the hyper-time variables. However, it remains a challenge work, due to the lack of effective solution methods, to…
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…
A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
Characterizing electromagnetic wave propagation in nonlinear and inhomogeneous media is of great interest from both theoretical and practical perspectives, even though it is extremely complicated. In fact, it is still an unresolved issue to…
Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of…
We consider elliptic solutions of the semi-discrete BKP equation and derive equations of motion for their poles. The basic tool is the auxiliary linear problem for the wave function.
Lie symmetry method is applied to investigate symmetries of the combined KdV-nKdV equation, that is a new integrable equation by combining the KdV equation and negative order KdV equation. Symmetries which are obtained in this article, are…
Family of equations, which is the generalization of the $K(m,m)$ equation, is considered. Periodic wave solutions for the family of nonlinear equations are constructed.
A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
The traditional method of factorization can be used to obtain only the particular solutions of the Li\'enard type ordinary differential equations. We suggest a modification of the approach that can be used to construct general solutions .…
The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves…
A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the…
wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.
We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrodinger (NLS) equation,…
Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained.
We present an analytical solution for triad nonlinear evolution equations with modified Schr\"odinger terms. An example for application in compressible water waves is presented.