Articles written in Pramana – Journal of Physics
Volume 81 Issue 3 September 2013 pp 367-376
Localized structures for $(2+1)$-dimensional Boiti–Leon–Pempinelli equation
Gui Mu Zhengde Dai Zhanhui Zhao
It is shown that Painlevé integrability of $(2+1)$-dimensional Boiti–Leon–Pempinelli equation is easy to be verified using the standard Weiss–Tabor–Carnevale (
Volume 83 Issue 4 October 2014 pp 473-480 Research Articles
Inclined periodic homoclinic breather and rogue waves for the (1+1)-dimensional Boussinesq equation
Zhengde Dai Chuanjian Wang Jun Liu
A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (1+1)-dimensional Boussinesq equation is used as an example to illustrate the effectiveness of the suggested method. Rational homoclinic wave solution, a new family of two-wave solution, is obtained by inclined periodic homoclinic breather wave solution and is just a rogue wave solution. This result shows that rogue wave originates by the extreme behaviour of homoclinic breather wave in (1+1)-dimensional nonlinear wave fields.
Volume 85 Issue 6 December 2015 pp 1063-1072
Rogue wave solutions of the nonlinear Schrödinger eqution with variable coefficients
Changfu Liu Yan Yan Li Meiping Gao Zeping Wang Zhengde Dai Chuanjian Wang
In this paper, a unified formula of a series of rogue wave solutions for the standard (1+1)-dimensional nonlinear Schrödinger equation is obtained through exp-function method. Further, by means of an appropriate transformation and previously obtained solutions, rogue wave solutions of the variable coefficient Schrödinger equation are also obtained. Two free functions of time 𝑡 and several arbitrary parameters are involved to generate a large number of wave structures.
Volume 87 Issue 2 August 2016 Article ID 0031 Research Article
Kink degeneracy and rogue potential solution for the (3+1)-dimensional B-type Kadomtsev--Petviashvili equation
ZHENHUI XU HANLIN CHEN ZHENGDE DAI
In this paper, we obtained the exact breather-type kink soliton and breather-type periodic soliton solutions for the (3+1)-dimensional B-type Kadomtsev--Petviashvili (BKP) equation using the extended homoclinic test technique. Some new nonlinear phenomena, such as kink and periodic degeneracies, are investigated. Using the homoclinic breather limit method, some new rational breather solutions are found as well. Meanwhile, we also obtained the rational potential solution which is found to be just a rogue wave. These results enrich thevariety of the dynamics of higher-dimensional nonlinear wave field.
Volume 89 Issue 5 November 2017 Article ID 0077 Research Article
Emergence and space–time structure of lump solution to the (2+1)-dimensional generalized KP equation
WEI TAN HOUPING DAI ZHENGDE DAI WENYONG ZHONG
A periodic breather-wave solution is obtained using homoclinic test approach and Hirota’s bilinear method with a small perturbation parameter $u_0$ for the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation. Based on the periodic breather-wave, a lump solution is emerged by limit behaviour. Finally, three different forms of the space–time structure of the lump solution are investigated and discussed using the extreme value theory.
Volume 97, 2023
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