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Article
Emergence and space–time structure of lump solution to the (2 \(+\) 1)-dimensional generalized KP equation
A periodic breather-wave solution is obtained using homoclinic test approach and Hirota’s bilinear method with a small perturbation parameter ...
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Article
Kink degeneracy and rogue potential solution for the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation
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 homoclin...
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Article
Rational homoclinic solution and rogue wave solution for the coupled long-wave–short-wave system
In this paper, a rational homoclinic solution is obtained via the classical homoclinic solution for the coupled long-wave–short-wave system. Based on the structures of ratinal homoclinic solution, the characte...
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Article
Rogue wave solutions of the nonlinear Schrödinger equation with variable coefficients
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 appropria...
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Article
Inclined periodic homoclinic breather and rogue waves for the (1+1)-dimensional Boussinesq equation
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 exam...
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Article
Localized structures for (2+1)-dimensional Boiti–Leon–Pempinelli equation
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 (WTC) approach after introducing the Kruskal’s simpli...