Articles written in Pramana – Journal of Physics
Volume 71 Issue 1 July 2008 pp 57-63 Research Articles
Bifurcation methods of dynamical systems for generalized Kadomtsov-Petviashvili-Benjamin-Bona-Mahony equation
By applying the bifurcation theory of dynamical system to the generalized KP-BBM equation, the phase portraits of the travelling wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth periodic waves converge to periodic cusp waves. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are obtained.
Volume 74 Issue 1 January 2010 pp 19-26 Research Articles
From bell-shaped solitary wave to W/M-shaped solitary wave solutions in an integrable nonlinear wave equation
Aiyong Chen Jibin Li Chunhai Li Yuanduo Zhang
The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.
Volume 80 Issue 3 March 2013 pp 471-478 Research Articles
Double compactons in the Olver–Rosenau equation
It is showed that the fully nonlinear evolution equations of Olver and Rosenau can be reduced to Hamiltonian form by transformation of variables. The resulting Hamiltonian equations are treated by the dynamical systems theory and a phase-space analysis of their singular points is presented. The results of this study demonstrate that the equations can support double compactons. The new Olver–Rosenau compactons are different from the well-known Rosenau–Hyman compacton and Cooper–Shepard–Sodano compacton, because they are induced by a singular elliptic instead of singular straight line on phase-space.
Volume 96 All articles Published: 13 October 2022 Article ID 0203 Research Article
Periods of periodic travelling wave solutions for an elastic beam equation
The periods of the periodic travelling wave solutions for an elastic beam equation were studied. By the transformation of variables, the elastic beam equation was reduced to a planar differential system. The period function of the planar differential system is examined. Itwas proved that the period function is a monotonic function.Moreover, the asymptotic behaviour of the period function was also given.
Volume 97, 2023
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