Multiple-Scale Solution of Initial-Boundary Value Problems for Weakly Nonlinear Wave Equations on the Semi-Infinite Line
S. C. Chikwendu, C. V. Easwaran
Source abstract
A multiple-scale perturbation solution of initial-boundary value problems for weakly nonlinear wave equations on the semi-infinite line is derived. The presence of both initial and boundary data requires the introduction of two new variables, a slow time and a slow space variable. It is shown that when the nonlinearities involve only first-order derivatives of the dependent variable, the leading-order solution is governed by two coupled first-order partial differential equations (PDEs). Examples are given to show that these PDEs can sometimes be solved to determine the leading-order solution.
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