Exact Solutions of DNLS and Derivative Reaction-Diffuson Systems

Jyh-Hao Lee, Yen-Ching Lee, Chien-Chih Lin
2002 Journal of Nonlinear Mathematical Physics  
In this paper, we obtain some exact solutions of Derivative Reaction-Diffusion (DRD) system and, as by-products, we also show some exact solutions of DNLS via Hirota bilinearization method. At first, we review some results about two by two AKNS-ZS system, then introduce Hirota bilinearization method to find out exact N-soliton solutions of DNLS and exact N-dissipaton solutions of the Derivative Reaction-Diffusion system respectively. called Resonance DNLS (RDNLS). RDNLS is equivalent to a
more » ... tive Reaction-Diffusion system by reciprocity relations [see Appendix]. In this paper, we obtain one and two dissipaton solutions of Derivative Reaction-Diffusion system and, as by-products, we obtain one and two soliton solutions of DNLS via Hirota bilinearization method [5, 6, 18] . At first, we review some results about 2×2 AKNS-ZS system [8, 9, 10, 12] , then we introduce Hirota bilinearization method to find out some exact soliton solutions of DNLS and dissipaton solutions of DRD system respectively. In this section, we review some results of 2×2 AKNS-ZS system. J.-H. Lee [8, 9, 10, 12] consider the following 2×2 system dM dx = z 2 [J, M ] + (zQ + P )M, Imz 2 = 0, Q ∈ L 1 (R, M 2 (C)), (2.1) where M (·, z) is bounded and continuous and P = QJ −1 Q. M (x, ·) is a meromorphic function with jump on = {z : Imz 2 = 0}. Let D z M = dM dx −z 2 [J, M ] and M ± (x, ·) be the limits of M on Ω + = {z : Imz 2 > 0}, Ω − = {z : Imz 2 < 0}. Then D z ((M − ) −1 M + ) = 0. So, there exists v(z) such that M + (x, z) = M − (x, z)e xz 2 J v(z)e −xz 2 J . (2.2)
doi:10.2991/jnmp.2002.9.s1.8 fatcat:qeiomqx4ovgdbgxt7unapjh35a