[PDF] Top 20 Bilinear approach to soliton and periodic wave solutions of two nonlinear evolution equations of Mathematical Physics

... analytic solutions for nonlinear evolution equations (NLEEs) is a key topic in the study of nonlinear phenomena ...Analytic solutions can help one to well understand the ... See full document

... differential equations (NLPDEs) are important mathematical models to describe physical ...of nonlinear physics, especially in soliton ...under nonlinear interac- tion and plays an ... See full document

... Abstract: Nonlinear mathematical models and their solutions attain much attention in soliton ...travelling wave solutions of foam drainage equation and NLEE of fourth ...these ... See full document

... Nonlinear evolution equations (NLEEs) play important roles in many areas of science, and their study goes back a very long ...exact solutions of NLEEs have been developed, including the ... See full document

... distributional approach is the most suitable one ...field equations. In the distributional approach one chooses special coordinates which are continuous along the singular hypersurface to avoid ... See full document

... Jimbo-Miwa equations. The search is going to be for a topological -soliton solution which is also known as a kink solution or a shock wave solu- ...following two subsections. For both ... See full document

... the two-dimensional periodic Volterra system with a period ...derive soliton solutions of arbitrary rank k and give a full classification of rank 1 ...exact solutions corresponding to ... See full document

... known as the Rabi cycle. The number of atoms that are in excitation level reaches its maximum when the frequency of the driving field matches the energy difference between the two levels. Using such ... See full document

... Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)–dimensional nonlin- ear evolution equation in much simpler way ... See full document

... They gave Green’s function to express the unique solution for the correspondence second- order functional differential equation with periodic boundary conditions and the functional dependence given by the piecewise ... See full document

... Inspired by the work of Li [5], we give sufficient conditions for the existence and uniqueness of the 2π -periodic solution of 1.1 by using the initial value problem method and homeomorphi[r] ... See full document

... The organization of this paper is as follows. In Section 2, we introduce some nota- tions and definitions, and state some preliminary results needed in later sections. We then study, in Section 3, the existence of ... See full document

... The paper is organized as follows. Section 2 is devoted to the proof of the existence of periodic solutions for problem (1.1) by using the Leray-Shauder fixed point theorem, which is di ff erent from that ... See full document

... I. When k  2 , n  1 , by substituting into (3) and (4) and (10), we get six principle equations. We mention that calculations are carried out by using MATHEMATICA where standard functions in calculus and algebra ... See full document

... where the nonlinearity f (u) was a real-analytic function near u =  with f () = f () = . Notice that the perturbation in [] satisfied special conditions and did not explicitly con- taining the space variables and the ... See full document

... Periodic solutions of di ff erence equations in Euclidean and Banach spaces have been con- sidered by many authors, see, for example, [1–3, 5–10, 12] and the references ...Mainly equations with ... See full document

... differential equations goes back to the 1970s with the Reebian ...differential equations we can cite the canards which appear in slow-fast vector fields and are closely related to the stability loss delay ... See full document

... In recent years, the existence of periodic solutions for second-order Li´enard equations u + f (u,u )u + g (u) = e(t,u,u ) (1.1) and its special case have been studied by many researchers, we refer ... See full document

... Where f ( )  is a solution of linear terms and the coefficients of the expansion a n ( n  1, 2,3,  ), should be determined. To deal with the nonlinear terms, we need to apply the extension of Cauchy’s product ... See full document

... the approach to solving the lump solutions of NLEEs use the Hirota bilinear form ...lump solutions and the interaction solutions [14]-[38] and breather waves [11], [39] of ... See full document