【摘 要】
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Nonstationary solutions of the Cauchy problem are found for a model equation that includes complicated nonlinearity,dispersion,and dissipation terms and can
【出 处】
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The Second bilateral conference between Russia and China Top
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Nonstationary solutions of the Cauchy problem are found for a model equation that includes complicated nonlinearity,dispersion,and dissipation terms and can de-scribe the propagation of nonlinear longitudinal waves in rods.Earlier,within this model,complex behavior of traveling waves has been revealed; it can be regarded as discontinuity structures in solutions of the same equation that ignores dissipationand dispersion.As a result,for standard self-similar problems whose solutions are constructed from a sequence of Riemann waves and shock waves with stationary structure,these solutions become multivalued.The interaction of counterpropagating(or copropagating)nonlinear waves is studied in the case when the corresponding self-similar problems on the collision of discontinuities have a nonunique solution.In addition,situations are considered when the interaction of waves for large times gives rise to asymptotics containing discontinuities with nonstationary periodic oscillating structure.
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