Soliton solutions of the Kadomtsev-Petviashvili II equation
نویسندگان
چکیده
We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form of its tau-function. We show that, in addition to previously known line-soliton solutions, this class also contains a large variety of new multi-soliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general, such solutions consist of unequal numbers of incoming and outgoing line solitons. From the asymptotic analysis of the taufunction, we explicitly characterize the incoming and outgoing line-solitons of this class of solutions. We illustrate these results by discussing several examples.
منابع مشابه
A generating function for the N-soliton solutions of the Kadomtsev-Petviashvili II equation
This work describes a classification of the N-soliton solutions of the Kadomtsev-Petviashvili II equation in terms of chord diagrams of N chords joining pairs of 2N points. The different classes of N-solitons are enumerated by the distribution of crossings of the chords. The generating function of the chord diagrams is expressed as a continued fraction, special cases of which are moment generat...
متن کاملMultiple Soliton Solutions of (2+1)-dimensional Potential Kadomtsev-Petviashvili Equation
We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived. Keywords—Hirota bilinear method, potential KadomtsevPetviashvili equation, Multiple sol...
متن کاملExact solutions of distinct physical structures to the fractional potential Kadomtsev-Petviashvili equation
In this paper, Exp-function and (G′/G)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. As a results, some new exact traveling wave solutions are obtained.
متن کاملoliton solutions of the Kadomtsev-Petviashvili II equation
We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II KPII equation by investigating the Wronskian form of its tau-function. We show that, in addition to the previously known line soliton solutions of KPII, this class also contains a large variety of multisoliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general...
متن کاملLine soliton interactions of the Kadomtsev-Petviashvili equation.
We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u(t)+6uu(x)+3u(xxx))(x)+u(yy)=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y-->infinity coincide with those of the N asymptotic line soli...
متن کامل