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Spectral method for solving nonlinear wave equations

Spectral method for solving nonlinear wave equations In this paper, we consider the following nonlinear wave equations: $$\begin{array}{l} \frac{{\partial ^2 \phi }}{{\partial t^2 }} - \frac{{\partial ^2 \phi }}{{\partial x^2 }} + \mu ^2 \phi + v^2 \chi ^2 \phi + f\left( {|\phi |^2 } \right)\phi = 0, \\ \frac{{\partial ^2 \phi }}{{\partial t^2 }} - \frac{{\partial ^2 \chi }}{{\partial x^2 }} + \alpha ^2 \chi + v^2 \chi |\phi |^2 + g(\chi ) = 0 \\ \\ \end{array}$$ with the periodic-initial conditions: $$\begin{array}{l} \phi (x---\pi ,t) = \phi (x + \pi ,t), \chi (x---\pi ,t) = \chi (x + \pi ,t), \\ \phi (x,0) = \hat \phi _0 (x), \phi _t (x,0) = \hat \phi _1 (x), \\ \chi (x,0) = \hat \chi _0 (x), \chi _t (x,0) = \hat \chi _1 (x), \\ - \infty< x< \infty , 0 \le t \le T. \\ \end{array}$$ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Spectral method for solving nonlinear wave equations

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References (5)

Publisher
Springer Journals
Copyright
Copyright © 1984 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF01669671
Publisher site
See Article on Publisher Site

Abstract

In this paper, we consider the following nonlinear wave equations: $$\begin{array}{l} \frac{{\partial ^2 \phi }}{{\partial t^2 }} - \frac{{\partial ^2 \phi }}{{\partial x^2 }} + \mu ^2 \phi + v^2 \chi ^2 \phi + f\left( {|\phi |^2 } \right)\phi = 0, \\ \frac{{\partial ^2 \phi }}{{\partial t^2 }} - \frac{{\partial ^2 \chi }}{{\partial x^2 }} + \alpha ^2 \chi + v^2 \chi |\phi |^2 + g(\chi ) = 0 \\ \\ \end{array}$$ with the periodic-initial conditions: $$\begin{array}{l} \phi (x---\pi ,t) = \phi (x + \pi ,t), \chi (x---\pi ,t) = \chi (x + \pi ,t), \\ \phi (x,0) = \hat \phi _0 (x), \phi _t (x,0) = \hat \phi _1 (x), \\ \chi (x,0) = \hat \chi _0 (x), \chi _t (x,0) = \hat \chi _1 (x), \\ - \infty< x< \infty , 0 \le t \le T. \\ \end{array}$$

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Apr 25, 2005

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