Search

A generalized Camassa-Holm equation with higher order nonlinear term was studied. First, we give a new blow-up criterion and a new blow-up phenomenon to the Cauchy problem for the equation under some conditions. Then, we focus on the analytical solutions for the equation. Finally, we prove the analyticity of solution for the equation. [ABSTRACT FROM AUTHOR]

Abstract: The local well-posedness and global solution for a modified periodic two-component Camassa–Holm system on the circle are established in the Sobolev space with , which are different from that of the two-component Camassa–Holm system. [Copyright &y& Elsevier]

Abstract: A shallow water equation including the Camassa–Holm and Degasperis–Procesi equations as special cases is investigated. Provided that initial value , and does not change sign, the existence and uniqueness of global weak solution for the equation are established. [Copyright &y& Elsevier]

Abstract: This paper is concerned with several aspects of travelling wave solutions for a (N+1) dimensional potential KdV equation. The Weierstrass elliptic function solutions, the Jaccobi elliptic function solutions, solitary wave solutions, periodic wave solutions to the equation are acquired under certain circumstances. It is shown that the coefficients of derivative terms in the equation cause the qualitative changes of physical structures of the solutions. [Copyright &y& Elsevier]

Abstract: The auxiliary differential equation approach and the symbolic computation system Maple are employed to investigate an -dimensional generalized Boussinesq equation. The exact solutions to the equation are constructed analytically under certain circumstances. It is shown that many of the solutions obtained in this work are new solutions. [Copyright &y& Elsevier]

Abstract: A nonlinear shallow water equation, which includes the famous Camassa–Holm (CH) and Degasperis–Procesi (DP) equations as special cases, is investigated. Provided that initial value , and does not change sign, it is shown that there exists a unique global weak solution to the equation. [ABSTRACT FROM AUTHOR]