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Explicit solutions of nonlinear wave equation systems - IOPscience
Explicit solutions of nonlinear wave equation systems. View the table of contents for this issue, or go to the journal homepage for more. 2013 Chinese Phys.

New exact solutions of nonlinear variants of the RLW, the PHI-four
Jul 21, 2012 ... wave (RLW) equation is an important nonlinear wave equation. Solitary ... shape function to construct an implicit finite element solution. The least ... system of algebraic equations with respect to aj, bj, b and c(where j = 1...M).

NONLINEAR WAVE EQUATIONS Contents 1. Introduction 1 2. 1+1
Aug 29, 2016 ... Local Existence for 1+1 Dimension Nonlinear Wave Equations. 8. 5. Energy and Global ... signs differ, the formula will be written explicitly. ... solution. Proof. The first step is to convert this to a first order system. [1. 0. 0 c2(t, x). ][ ...

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IJNS Vol23 No3 Paper 6-Explicit.pdf

On Some Exact Solutions of Nonlinear Wave Equations
description of these additional conditions in the explicit form is a difficult ... classes of exact solutions to nonlinear equations of mathematical physics. .... Thus, if we construct all solutions to system (6), hence we get the set of all values of.

Exact solutions of nonlinear partial differential equations - OPUS 4
into an overdetermined system for the purpose of obtaining explicit solutions. ... on finding exact solutions to semilinear wave equations and heat equations with  ...

Exact solitary wave solutions of nonlinear wave equations
Writing the solitary wave solutions of a nonlinear wave equation as the ... The system can be solved via Wu Elimination or GrSbner base method. ..... Shang, Y. D. , Explicit and exact solutions for a class of nonlinear wave equations, Acta Appl.

For instance, the nonlinear wave phenomena observed in fluid dynamics ... of the exact solutions for some nonlinear partial differential equations such as the cubic .... matica, we solve the system of algebraic equation which obtained in step 4 with ..... construct new explicit exact solutions for the approximate equations for.

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exact solutions of some nonlinear systems of partial differential equations, including, ... Thus, it is important to investigate the exact explicit solutions of nonlinear.

Higher Order Nonlinear PDE's
conclude that this diffusion equation has no interesting TW solutions. Similarly, ... In this example, an explicit analytical solution for f(z) is possible. ... between the linear and nonlinear problems that the wave speed for the linear equations .... The closed orbits represent periodic solutions to the first order dynamical system.

Exact Solutions of Nonlinear Partial Differential Equations The Tanh
tions of nonlinear (systems) of partial differential equations (PDEs) and differential-difference equations (DDEs, lattices). • Solutions of tanh or sech type model solitary waves in fluid dy- ...... Look at other types of explicit solutions involving.

Some New Solutions of Shallow Water Wave Equation - CiteSeerX
As a result, more explicit traveling wave solutions involving arbitrary param- eters are found ... flow, signal processing, system identification, control theory, finance, and fractional ... exact solutions of these nonlinear partial differential equations.
paper id-21201486.pdf

A procedure to construct exact solutions of nonlinear evolution
Exact solutions; the functional variable method; nonlinear wave equations. PACS Nos 02.30. ... Various methods for obtaining explicit solutions of non- ... systems like Maple which allows us to perform some complicated and tedious alge-.

Symbolic Computation and Construction of New Exact - De Gruyter
... Wave. Solutions to Fitzhugh-Nagumo and Klein-Gordon Equations ... Periodic and solitary traveling wave solutions capable of ... ing for explicit solutions of nonlinear evolution equa- tions by ... Periodic wavetrains are found in many systems.

Chapter 22 Nonlinear Partial Differential Equations - math.umn.edu
Dec 11, 2012 ... inherently linear theory, most real-world physical systems, including gas ... wave solutions to the limiting first order dispersionless equation, ..... we note that, at t = 0, the implicit solution formula (22.16) reduces to u(0,x) = f(x).

A multiple exp-function method for nonlinear differential equations
Oct 16, 2010 ... Multiple wave solutions, Integrable equations, Solitons. 1 Introduction .... will also work for systems of nonlinear equations and high-dimensional ones. ... The explicit solutions (2.3) offer reasons why the approach is called the.

Reduction Operators and Exact Solutions of Variable - MDPI
Dec 22, 2016 ... of variable coefficient nonlinear wave equations with power nonlinearities, .... The system Q(2) consists of (7) and the equations obtained by t- and ...... )2r2, then the general solution of (42) can be written in the implicit form: ∫.

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Sep 8, 2000 ... Exact solutions of reaction-diffusion systems and nonlinear wave equations ... Explicit solutions of Fisher's equation for a special wave speed.

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auxiliary -equation method for nonlinear physical systems ... wave solutions of some physical systems in terms of these new solutions of the variable- ..... [10] T. Özis, I. Aslan, Exact and explicit solutions to the (3+1)-dimensional Jimbo–Miwa ...

Exact and explicit solutions to nonlinear evolution equations using
Our method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are derived  ...