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Solitary wave solutions of a fourth-order bidirectional dispersive nonlinear wave equation
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Abstract
A fourth-order one-dimensional nonlinear dispersive wave equation arising in generalized elastic solids is considered. This equation includes the regularized Boussinesq equation and the double dispersion equation as special examples. A particular parameter regime for which the equation possesses solitary wave solutions is determined and an exact solitary wave solution is found. Approximate equations governing unidirectional propagation of long acoustic waves and short optic wave packages are derived using formal asymptotic expansions. Parameter conditions for which the resulting equations have solitary wave solutions are found and exact solitary wave solutions of the approximate equations are presented.
Title: Solitary wave solutions of a fourth-order bidirectional dispersive nonlinear wave equation
Description:
Abstract
A fourth-order one-dimensional nonlinear dispersive wave equation arising in generalized elastic solids is considered.
This equation includes the regularized Boussinesq equation and the double dispersion equation as special examples.
A particular parameter regime for which the equation possesses solitary wave solutions is determined and an exact solitary wave solution is found.
Approximate equations governing unidirectional propagation of long acoustic waves and short optic wave packages are derived using formal asymptotic expansions.
Parameter conditions for which the resulting equations have solitary wave solutions are found and exact solitary wave solutions of the approximate equations are presented.
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