Specific solutions of the generalized Korteweg-de Vries equation with possible physical applications

Paul Bracken 1
  • 1 Department of Mathematics, University of Texas, 1201 W. University Dr., 78541-2999, Edinburg, USA

Abstract

Solutions for a type of generalized Korteweg-de Vries equation which should have physical impact will be determined here. These types of solutions should have applications in the study of intrinsic localized modes optical waveguide arrays and fluid dynamics. It is shown that trigonometric and hyperbolic solutions can be obtained by matching powers and coefficients of the independent terms in the equation after the assumed solution has been substituted. As well, solutions to the equation in terms of more complicated Jacobe elliptic functions are determined.

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