Articles written in Pramana – Journal of Physics
Volume 89 Issue 5 November 2017 Article ID 0077 Research Article
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 94 All articles Published: 30 January 2020 Article ID 0036 Research Article
A lump-type solution of the (2 + 1)-dimensional generalised fifth-order Korteweg–de Vries (KdV) equation is obtained from the two-soliton solution by applying the parametric limit method. Some theorems and corollaries about the superposition behaviour between lump solutions and different forms of $N$-soliton ($N \rightarrow\infty$) solutions are constructed, and detailed proofs are given. Besides,we give a large number of examples and spatial evolution graphics to illustrate the effectiveness of the described theorems and corollaries. Some new nonlinear phenomena and superposition behaviour, such as rational-exponential type, rational-cosh-cos type, rational-sin type, rational-logarithmic type etc., are simulated and shown for the first time. Finally, we also illustrate the superposition between high-order lump-type solutions and $N$-soliton solutions.
Volume 94, 2020
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