NOTE: Special Solutions to Nonlinear Difference-Differential Equations

✍ Scribed by Kazuaki Narita

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 108 KB
• Volume: 205
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1996.5171

✦ Synopsis

In a previous paper, we presented new difference-differential equations, and studied their N-soliton solution, elliptic function solutions, and 1-soliw x ton solution under a nonvanishing boundary condition at the infinity 1 . In this note, we present new special solutions for the above equations which cannot be obtained from known solutions through the transformation. We also study the corresponding physical solutions for the new equations derived from the above equations through seven different transformations. Recently, Shabat and Yamilov have presented various new solvable differw x ence-differential equations 2᎐4 . We also make reference to the connection between their equations and our transformed equations.

Ž . Ž . w x First, we remark that Eqs. 1.7 , 2.3 of 1 are rewritten through the