[PDF] Top 20 N Fold Darboux Transformation for a Nonlinear Evolution Equation

... eral nonlinear evolution equations. For a special case, we give the N-fold ...the N-fold Darboux matrix and the relationship between new and old ...the nonlinear ... See full document

... explaining nonlinear phe- nomena such as nonlinear optics effect, fusion reaction in plasma physics, superconduc- tion phenomenon, magnetohydrodynamic phenomenology, ...differential-difference equation ... See full document

... The acoustic problem (1.1) is also interesting from the integrable systems viewpoint. (The references quoted to this effect represent just a tiny fraction of the vast body of literature on the subject. In particular, we ... See full document

... The multivalued solutions obtained in Section 3.3 obviously mean that the study of the VE (11) in the original coordi- nates (𝑥, 𝑡) leads to certain difficulties. These difficulties can be avoided by writing down the VE ... See full document

... tial equation. Especially, some results on the Hirota equation are proposed by analytical [–] and numerical [] ...this equation. This paper is organized as fol- lows. The Lax pair and ... See full document

... equation – VE) that can be integrated by the inverse scattering transform (IST) method. This equation arose as a result describing the high-frequency perturbations in a relaxing medium. The VE has two ... See full document

... dimensional nonlinear partial differential or difference equations attract much ...and Darboux transformation ...KP equation, but others are deduced firstly from (1 + 1) dimensional ... See full document

... auxiliary equation method, many kinds of smooth type soliton, tense type soliton and peak soliton and so on new solutions of the nonlinear evolution equations have been obtained ...function ... See full document

... NLS equation () by using the generalized Darboux transformation, then analyze the rogue wave through their ...NLS equation and point out the connection between RW and modulation ... See full document

... Abstract: Nonlinear mathematical models and their solutions attain much attention in soliton ...drainage equation and NLEE of fourth ...these nonlinear differential equations. Wave ... See full document

... with Darboux-Lax repre- sentation between Grassmann extensions of algebraic ...of Darboux transformations, we first derive a Dar- boux matrix associated with the Grassmann-extended derivative ... See full document

... ear evolution equation in much simpler way in comparison to other existing ...of nonlinear evolution equation and using this bilinear form, bilinear B¨ acklund transformations and ... See full document

... integer-order evolution equation, and used to model problems in physics, neurons, hydrology, viscoelasticity and rheology, image processing, mechanics, mechatronics, finance and con- trol theory, see ... See full document

... of nonlinear partial differential equations in modelling physical phenomena has become an important ...B¨acklund transformation[11], Exp-function method[12, 13, 14, 15, 16] and so ...of nonlinear ... See full document

... In Equation (1), the nonlinear term brings a self-induced potential of the form V x z ( ) , = u x z u ( ) ( , ∗ − x z , ) , which satisfies the PT symmetric condition V x z ( ) , = V ∗ ( − x z , ) ...of ... See full document

... We study the exact solutions of the JM Equation 1.1 by using Darboux transformation DT, which is an effective method to get exact solutions from the trivial solutions of the nonlinear pa[r] ... See full document

... studying nonlinear equa- tion, and it also produces various methods to solve soliton equations, such as the inverse scattering method [7] [8] [9], the nonlinear method [10] [11], Hirota bi- linear method ... See full document

... functions of space variables, and they are associated with complex eigenvalues of the as- sociated spectral problems []. It is worth pointing out that our results seem to be differ- ent from those reported in [] ... See full document

... the nonlinear models in shallow water wave is very important, such as Korteweg-de Vries (KdV) equation [1] [2], Kadomtsev-Petviashvili (KP) equation [3] [4], Boussinesq equation [5] [6], ... See full document

... of nonlinear physical ...of nonlinear equations still have drawn a lot of interest by diverse group of ...Riccati equation [10], the Jacobi elliptic function expansion method [11, 12], the Hirota’s ... See full document