Download or read book Generalized Darboux Transformation and Nth Order Rogue Wave Solution of a General Coupled Nonlinear Schrödinger Equations written by Mariya Makaryan and published by . This book was released on 2016 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear partial differential equations (NLPDEs) are extremely hard to solve analytically because no specific general algorithm exists for this task. As is well known, integrability of the NLPDEs plays an important role in soliton theory (when the solutions exist, they help to understand the phenomena modeled by these NLPDEs), which can be regarded as a pretest and the first step of its exact solvability. Among the properties that can characterize the integrability of NLPDEs are: the bilinear representation, Bäcklund transformation (BT), Lax pair, infinitely many conservation laws, infinite symmetries, Hamiltonian structure, Painleve test and so on. A NLPDE is said to be completely integrable in the sense of Lax if it can be written as a system of linear PDEs in an auxiliary function under the condition that the original NLPDE satisfies a compatibility condition. In this thesis, Lax-pair and generalized Darboux transformation (GDT) method are constructed for the generalized coupled nonlinear Schrödinger equations (GCNLSEs). Using the GDT method, the recur- sive formula for the Nth-order rogue wave solution for the GCNLSEs is derived and the Nth-order determinant representation for these equations is given. From the recursive formula, the first-, second-, and third-order rogue wave solutions with certain free parameters are obtained. Based on the Darboux transformation, breather solutions for the GCNLSE are derived as well. Moreover, the dynamical features of these solutions are graphically discussed and the modulation instability of GNLSEs is investigated.