Higher order Peregrine breathers solutions to the NLS equation

[摘要] The solutions to the one dimensional focusing nonlinear Schrodinger equation (NLS) can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N + 1) in x and t. These solutions depend on 2N - 2 parameters : when all these parameters are equal to 0, we obtain the famous Peregrine breathers which we call PNbreathers. Between all quasi-rational solutions of rank N fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at point (x = 0,t = 0), the PNbreather is distinguished by the fact that PN(0, 0) = 2N + 1. We construct Peregrine breathers of the rank N explicitly for N ≤ 11. We give figures of these PNbreathers in the (x; t) plane; plots of the solutions PN(0; t), PN(x;0), never given for 6

[发布机构] Université de Bourgogne, Dijon, France^1

[效力级别] 数学

[关键词] Absolute values;Focusing nonlinear Schrodinger equation;Higher-order;NLS equations;Rational solution