Publication: Nonlinear Transverse Waves in a Generalized Elastic Solid and the Complex Modified Korteweg–deVries Equation
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IOP Publishing
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Abstract
Summary: By using an asymptotic expansion technique based on Lagrangian density formulation, we demonstrate that the nonlinear interaction between two transverse waves propagating in a generalized elastic solid can be described asymptotically by the complex modified Korteweg-de Vries (CMKdV) equation. Also, the CMKdV equation is shown to be Hamiltonian, and its solitary wave solutions are investigated by means of a modified Hirota method.
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Physica Scripta
ISSN
0031-8949
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CLOSED
Keywords
asymptotic expansion, KdV equations (Korteweg-de Vries equations), Lagrangian density formulation, nonlinear interaction between transverse waves, Solitary waves in solid mechanics, Nonlinear waves in solid mechanics, solitary wave, modified Hirota method, complex modified Korteweg-de Vries equation, Hamiltonian form of equation, Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics