The existence of a traveling wave with special properties to modified KdV and BKdV equations is proved. Nonlinear terms in the equations are defined by means of a function f of an unknown u satisfying some conditions.
In this paper, travelling wave solutions for the Zakharov equation in plasmas with power law nonlinearity are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given.
In this paper, we study a class of Initial-Boundary Value Problems proposed by Colin and Ghidaglia for the Korteweg-de Vries equation posed on a bounded domain (0,L). We show that this class of Initial-Boundary Value Problems is locally well-posed in the classical Sobolev space Hs(0,L) for s > -3/4, which provides a positive answer to one of the open questions of Colin and Ghidaglia [Adv. Differ. Equ. 6 (2001) 1463–1492].