Soliton solutions of a coupled Korteweg-de Vries equation

A Direct Transformation Method and its Application to Variable Coefficient Nonlinear Equations of Schrödinger Type

“…Using Theorem 2 and the known solutions of (20) [31], we can give exact nontravelling wave solutions of (13) as follows. Case 1.…”

“…0932-0784 / 09 / 1100-0697 $ 06.00 c 2009 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com On the other hand, directly seeking for exact solutions of nonlinear partial differential equations (NLP DEs) has become one of central theme of perpetual interest in mathematical physics and many effective methods have been presented such as inverse scattering method [8,19], Hirota's bilinear method [20], Backlund transformation method [21], Painleve expansion method [22], and so on. Recently, based on the computer system like Maple or Mathematica, many powerful algebraic methods, which include sinecosine method [23], the Riccati equation expansion method [24], the Jacobi elliptic function expansion method [25], exp method [26], and so on [27 -31], have been proposed and applied to derive many exact solutions of NLPDEs.…”

An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves

“…In a study Eq. (1) is converted to a new complex coupled KdV equation [41] and the Hirota-Satsuma equation [13] by putting w = v * and w = v respectively. Further Eq.…”

Comment: On a recently proposed relation between oHS and Ito systems

“…The author of [1] points out that there is a printing error in the conserved density I 3 (instead of 1 + a there is a) obtained in [2].But this claim is wrong and I 3 in the ref. [3] is correct as it is.…”

“…It is well known that the original Hirota-Satsuma system (oHS) [2] u t = a(u xxx + 6uu x ) + 2bvv x ,…”