The integral bifurcation method and its application for solving a family of third-order dispersive PDEs

Rui, Weiguo; He, Bin; Ye, Long; Chen, Can

doi:10.1016/j.na.2007.06.027

Cited by 49 publications

(35 citation statements)

References 28 publications

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“…(1.1) are not studied yet under the above parametric conditions. In this paper, by using a improved method named the integral bifurcation method [10,11], we shall investigate all kinds of singular travelling wave solutions and their dynamic characters…”

Section: Introductionmentioning

confidence: 99%

Some new travelling wave solutions with singular or nonsingular character for the higher order wave equation of KdV type (III)

Rui

2009

Nonlinear Analysis: Theory, Methods & Applications

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Section: Introductionmentioning

confidence: 99%

Some new travelling wave solutions with singular or nonsingular character for the higher order wave equation of KdV type (III)

Rui

2009

Nonlinear Analysis: Theory, Methods & Applications

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“…As far as we know, it is applied by Li and Liu (2000) for the first time, then followed by many good results (Long, Rui and He, 2005;Li et al, 2006;He et al, 2008;Rui et al, 2008;Chen et al, 2015;Chen and Tang, 2006) and references therein. However, there exists a premise condition in the above applications of this method, namely the dispersive equation can be transformed into an integrable planar system via certain travelling-wave solution ansatz, and more to obtain a integrable system is usually challenging, because there is no fixed method confirming us to find integrable conditions or its first integrals for a general planar system.…”

Section: ∂U (X T)mentioning

confidence: 99%

Exact wave solutions for a class of single-species model of population dynamics

Wang

2017

IJDSDE

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Abstract:In this paper, exact wave solutions to the single-species population dynamical model with density-dependent migrations and Allee effect are studied. First, the non-linear evolution equation is reduced to a planar system by transformation of variables, then based on the planar dynamical systems theory, its first integral is determined by computing singular point quantities, and a phase-portrait analysis of its singular points is presented. From this, some explicit expressions of the bounded travelling-wave solutions are obtained for the single-species model, which correspond to the real patterns of spread during biological invasions. In terms of the technique of finding exact travelling-wave solutions of a non-linear partial differential equation, the work is new.Keywords: exact solution; integrability; population dynamical model; singular point quantity.Reference to this paper should be made as follows: Wu, H., Li, J. and Wang, Q. (2017) 'Exact wave solutions for a class of single-species model of population dynamics', Int.

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“…Using the integral bifurcation method [8,9], Eq. (4) can be rewritten as the following system: άφ ας αν 2v 2 (6) where φ 5 -3(cv -β)/{αν).…”

Section: New Periodic Loop Solitons With Local Energy Loss Of the Genmentioning

confidence: 99%

“…[5], by using the bifurcation theory of dynamic system, the compactons, solitary waves, smooth and nonsmooth periodic waves with peaks as well as the existence conditions have been presented. In this paper, the semi-inverse method [6,7] and the integral bifurcation method [8,9] will be used to study Eq. (1).…”

Section: Introductionmentioning

confidence: 99%