Solitons and periodic travelling waves for the 2D-generalized Benney–Luke equation

Abstract

This article is related with one direction periodic travelling waves solutions for the 2D generalized Benney–Luke equation

i.e, solution of the form Φ(x,y,t)= u(x−ct, y), with ζ =x−ct periodic. We establish the existence of a family of x-periodic travelling wave solutions for c ²<min {1, a/b}. We show that a special sequence of this family is uniformly bounded in norm and converges to a lump soliton in (solitary wave of finite energy) in an appropriate sense.

Keywords:

• 2D water model
• Travelling waves
• Solitons
• Periodic approximation
• Variational methods

Keywords:

• 2000 Mathematics Subject Classifications
• 35Q35
• 35B10
• 35Q51
• 35A15

Acknowledgments

This work is partially supported by Colciencias (grant # 1106-05-16858) Colombia and Universidad del Valle, Cali, Colombia. The author is thankful with the ICTP Math Group (Trieste-Italy) for the invitation during July–August 2006.