Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential

• 来源期刊: 中国物理（英文版）
• 学科: 物理学
• 关键词: bifurcation solitary waves nonlinear wave equation
• 年，卷（期）: 2002,（6）
• 页码范围: 547-552
• 页数: 6页
• 分类号: O4
• 语种: 英文

摘要

For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.