Rogue Waves of the Lakshmanan Porsezian Daniel Equation Depending on Multi-parameters
Pierre Gaillard *
Université de Bourgogne Franche Comté, Institut de mathématiques de Bourgogne, 9 Avenue Alain Savary BP 47870 21078 Dijon Cedex, France.
*Author to whom correspondence should be addressed.
Abstract
Quasi-rational solutions to the Lakshmanan Porsezian Daniel equation are presented. We construct explicit expressions of these solutions for the first orders depending on real parameters. We study the patterns of these configurations in the (x, t) plane in function of the different parameters. We observe in the case of order 2, three rogue waves which move according to the two parameters. In the case of order 3, six rogue waves are observed with specific configurations moving according to the four parameters.
Keywords: Lakshmanan Porsezian Daniel equation, quasi-rational solutions