Two-dimensional wave propagation in a generalized elastic solid

Babaoglu C., Erbay S.

CHAOS SOLITONS & FRACTALS, vol.12, no.2, pp.381-389, 2001 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 2
  • Publication Date: 2001
  • Doi Number: 10.1016/s0960-0779(99)00182-4
  • Journal Name: CHAOS SOLITONS & FRACTALS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.381-389
  • Istanbul Technical University Affiliated: No

Abstract

The object of the present study is to investigate the propagation of two-dimensional waves in a weakly nonlinear and weakly dispersive elastic solid. The reductive perturbation method is directly applied to a Lagrangian whose Euler-Lagrange equations give the field equations for a quadratically nonlinear elastic medium with higher order gradients. In the long-wave approximation, it is shown that the long-time behavior of the two transverse waves is governed by the two coupled modified Kadomtsev-Petviashvili (CMKP) equations. Depending on the choice of the direction of perpendicular dynamics, various forms of the CMKP equations are obtained. Some special solutions are also presented for a simplified form of the CMKP equations. (C) 2000 Elsevier Science Ltd. All rights reserved.