【摘要】 用动力系统理论、分支理论和直接方法,研究了广义正则长波方程(GRLW),证明该方程存在光滑孤立波解和无穷多光滑周期波解。求出了当m=1时GRLW方程的显式精确行波解,并在不同的参数条件下,给出了上述光滑孤立波解和无穷多光滑周期波解存在的各类充分条件。更多还原

【Abstract】 The theory of dynamical systems,the theory of bifurcation,and the direct method are referred to in investigating the generalized and the regularized long wave equation（GRLW）.u_t+u_x+u^mu_x-μu_xxt=0.Under the condition g≠0,where g is the integral constant,the existence of smooth solitary wave solutions and uncountable infinite smooth periodic wave solutions are proved.When m=1,some exact explicit parametric representations of traveling wave solutions of GRLW equations are obtained.Under different parametric conditions,various sufficient conditions to guarantee the existence of the above solutions are given.更多还原