Read online On Solutions of Nonlinear Wave Equations (Classic Reprint) - Joseph Bishop Keller | PDF
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Restrictions on the parameters, we prove that every weak solution to system above blows up in nite time, provided the initial energy is negative. Wave equations under the in uence of nonlinear damping and nonlinear sources have generated considerable interest over recent years.
In section 2, we describe this method for finding exact travelling wave solutions of nonlinear evolution equations.
Initial and boundary value problems of wave equations with nonlinear perturbation will be discussed. The non-existence of solutions for the above problems primarily depends upon the structure of nonlinear perturbation. Some sufficient conditions for the non-existence of global solutions of the above problems will be derived.
As a preliminary definition, a soliton is considered as solitary, traveling wave pulse solution of nonlinear partial differential equation (pde).
Solitary wavessolitary waves are fundamental solutions of nonlinear, dispersive equations including the euler equations. It is therefore important for all approximate wave models to possess solitary wave solutions that are similar to the euler solitary waves.
We consider the cauchy problem for nonlinear abstract wave equations in a hilbert space. Our main goal is to show that this problem has solutions with arbitrary positive initial energy that blow up in a finite time. The main theorem is proved by employing a result on growth of solutions of abstract nonlinear wave equation and the concavity method.
A non-exhaustive selection of well known 1d nonlinear wave equations and their closed-form solutions is given below. The closed form solutions are given by way of example only, as nonlinear wave equations often have many possible solutions.
This paper is presented to give numerical solutions of nonlinear wave-like equations with variable coefficients by using reduced differential transform method.
Solutions to various nonlinear partial differential equations from soliton theory. For a review of other direct methods we refer to papers by hereman [20] and hereman and takaoka [21]. The method also allows testing if a certain equation satisfies the necessary requirements to admit solitary wave solutions and soliton solutions.
Exact solutions of nonlinear evolution equations (nlees) are very crucial to realize the obscurity of many physical phenomena in mathematical science. The modified simple equation (mse) method is especially effective and highly proficient mathematical instrument to obtaining exact traveling wave solutions to nlees arising in science, engineering and mathematical physics.
This article studies the cauchy problem for systems of semi-linear wave equations on $\mathbbr^3+1$ with nonlinear terms.
The dynamical model of a nonlinear wave is governed by a partial differential equation which is a special case of the b-family equation.
18 nov 2020 pdf we apply the (g'/g)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions.
2001 on solutions of nondegenerate wave equations with nonlinear damping terms jeong ja bae jong yeoul park differential integral equations 14(12): 1421-1440 (2001).
Furthermore, traveling wave solutions are obtained by employing the (g'/g)-expansion method. Many phenomena in the real world are often described by nonlinear evolution equations (nlees) and therefore such equations play an important role in applied mathematics, physics, and engineering.
A new methodology is developed in this work to solve a one-dimensional (1d) nonlinear wave propagation problem. In its response, the space variable is converted to time functions at different.
Pdf we present the adomian decomposition method for a nonlinear wave equation subject to the initial conditions.
Then to derive an a priori estimate for uε t where uε is a solution of the approximate.
This paper elucidates the main advantages of the exp-function method in finding exact solutions of nonlinear wave equations.
Periodic solutions of a boundary-value problem for a large class of nonlinear scalar wave equations. The argument is inspired by a method introduced in [8], where families of complex valued tensor elds were used to construct stationary black hole solutions of the einstein equations.
An analytic solution of a nonlinear wave equation in the form of a series with easily computable components using the decomposition method will be determined.
Initial and boundary value problems of wave equations with nonlinear perturbation the non-existence of solutions for the above problems primarily depends.
The closed form solutions are given by way of example only, as nonlinear wave equations often.
It is based on the taylor series, except that adomian decomposition method expands the solution about a function, instead of a point.
The nonlinear wave equation with variable long wave velocity and the gordon-type equations (in particular, the ϕ4-model equation) display a range of symmetry generators, inter alia, translations, lorentz rotations and scaling - all of which are related to conservation laws.
In the subsequent chapter, we explore the existence of global solutions, in particular for small initial data.
We investigate the exact travelling wave solutions of the nonlinear schrödinger equation using three methods, namely, the auxiliary equation method, the first integral method, and the direct integral method.
Abstract a method is proposed for obtaining traveling‐wave solutions of nonlinear wave equations that are essentially of a localized nature. It is based on the fact that most solutions are functions of a hyperbolic tangent. This technique is straightforward to use and only minimal algebra is needed to find these solutions.
The nonlinear wave equation also admits nonlinear waves that propagate to the right and to the left, but being non-linear, superposition fails, and a general solution does not exactly decompose into a sum of left and right going waves as do solutions of the linear (constant c) wave equation.
Ghoreishi et al [6] solved nonlinear wave-like equations with variable coefficients using the adomian decomposition method, while ramadan and al-luhaibi [11] determined the solution of nonlinear.
We present the adomian decomposition method for a nonlinear wave equation subject to the initial conditions.
Loosely speaking, the genus g solution can be viewed as a ‘nonlinear superposition’ of g+1 nonlinear modes (including the trivial, plane wave mode). As was mentioned in the introduction, the fnls solutions traditionally considered as ‘analytical prototypes’ of rogue waves are the ab, km breather and their limiting case, the peregrine.
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