Explicit Solitary Wave Solutions Research Articles

New exact and explicit solitary wave solutions to a class of coupled nonlinear equations

New exact and explicit solitary wave solutions are obtained for the coupled nonlinear equation by using a simple way of making the ansatz u( χ, t) = As ech n + A 0 with = k( χ + wt) + 0.

NEW SOLITARY WAVE SOLUTIONS FOR A CLASS OF FIFTH-ORDER NOLINEAR EVOLUTION EQUATIONS

The exact explicit solitary wave solutions for a class of fifth-order nonliear evolution equations are obtained by using a homogeneous method. Particular important cases of the equation, such as Kaup-Kupershmidt, Caudrey-Dodd-Gibbon-Sawada-Kotera and fifth-order KdV equations can be solved by this method.

Exact and explicit solitary wave solutions to some nonlinear equations

Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative Φ4-model equation, the generalized Fisher equation, and the elastic-medium wave equation.

SOLITARY WAVE SOLUTIONS TO THE 2N+1 ORDER KdV-TYPE EQUATIONS

In this paper, explicit and exact solitary wave solutions to the 2N+1 order KdV-type equations are given. The higher order generalized KdV equation(GKdVE), the higher order generalized MKdV equation (GMKdVE), and the higher order generalized Schamel's MKdV equation(GSMKdVE) are covered by these equations. Moreover, 2N+1 order KP-type equation is discussed.

New explicit exact solitary wave solutions for a new Hamiltonian amplitude equation

In this Letter, new explicit exact solitary wave solutions for a new Hamiltonian amplitude equation are obtained.

On a class of solitary wave solutions of atmospheric nonlinear equations

In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the presence of specific forcing exhibit the exact and explicit solitary wave solutions under certain conditions.

Implicit solitary wave solutions of the generalized magma equation

The generalized magma equation, in which dispersion and nonlinearity are coupled together in a manner reminiscent of the Harry-Dym equation, is solved to indicate both periodic and aperiodic implicit solitary wave solutions. It is argued that the presence of an additional spatial derivative in the magma equation also permits explicit solitary wave solutions, a feature not shared by the Harry-Dym equation.

A Higher Order (2+1)-Dimensional Korteweg-de Vries Equation and Its Exact Solitary Wave Solutions11The project supported by National Natural Science Foundation of China.

The (2+1)-dimensional Korteweg-de Vries (KdV) equation proposed recently by Levi is extended to a higher order (2+1)-dimensional KdV equation from water wave dynamics when considering surface tension. Its exact and explicit solitary wave solutions can be obtained by relating it to the higher order KdV equation.

Cylindrical envelope solitary waves

The method of multiple-scales is used to investigate the nonlinear modulation of capillary-gravity waves with cylindrical symmetry. We find that the evolution of wave-packets is described by a nonlinear Schrödinger-like equation i(U + U/2τ) + αUξξ + β|U|2U = 0. Some exact and explicit cylindrical envelope solitary wave solutions are also obtained by means of variable transformations.

A set of exact and explicit solitary wave solutions for a class of generalized KdV equations with arbitrary odd order derivatives (A sieving method in a closed function class)

Recent higher order KdV equations are interesting for physics, for example when the surface tension approaches close to a certain value. In this paper using the method of sieving in a closed function class, a set of exact and explicit solitary wave solutions with a unified form are given to higher order or generalized higher order KdV equations with 7th, 9th or arbitrary odd order derivatives, when their parameters satisfy some suitable restricted conditions.

Exact and explicit solitary wave solutions to a model equation for water waves

Exact and explicit solitary wave solutions are obtained for the higher order Korteweg-d Vries equaion, which has been obtained recently in a formal asymptotic approximation for water waves with surface tension.

Exact and explicit solitary wave solutions for the generalised fisher equation

The exact and explicit solitary wave solutions for the generalized Fisher equation ∂u ∂t − ∂ 2u ∂x 2 − ( m u )( ∂u ∂x ) 2=u(1−u α) are obtained via introducing nonlinear transformations. The method used in this work can be applied to other nonlinear equations. The method here is very concise and primary. The solutions can effectively be used to discuss related nonlinear problems in physics and biophysics.