New kinds of solutions to Gardner equation

“…Eq. (4) is studied in [1][2][3] where new kind of solutions were obtained. Gardner equation is widely used in various branches of physics, such as plasma physics, fluid physics, quantum field theory [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

New solitons and kink solutions for the Gardner equation

Wazwaz

2007

Communications in Nonlinear Science and Numerical Simulation

240

123

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“…is a still undetermined function of the independent variables X ≡ (x 0 = t, x 1 , x 2 , ··· , x m )], the projective Riccati equation [9,10] is defined by…”

Section: Novel Solutions Of the (2+1)-dimensional Gbk Systemmentioning

confidence: 99%

“…First, the dromion has been studied intensively for this system. Second, a special procedure, named here as the mapping approach [8] via a projective Riccati equation [9,10], is established and will lead to exact solutions for the (2+1)-dimensional GBK system. By choosing elementary functions as the building blocks in this algorithm, various localized solutions can be found.…”

Section: Introductionmentioning

confidence: 99%

Some Coherent Excitations for the (2+1)-Dimensional Generalized Broer-Kaup System

Liu

2006

Zeitschrift Für Naturforschung A

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Using a projective Riccati equation, several types of solutions of the (2+1)-dimensional generalized Broer-Kaup system are obtained, including multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. From these, two sets of wave packets are expressed as rational functions of elliptic functions. Especially, peculiar wave patterns that are localized in one direction but periodic in the other direction arise by taking the long wave length limit in one spatial variable. Also exponentially localized wave patterns, which differ from the known dromions, are obtained by taking the long wave length limit in both spatial variables. The interactions of two dromions with inelastic and elastic behaviors are presented.

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“…Eq. (1) is widely used in various fields of physics, such as solid-state physics, plasma physics, fluid physics and quantum field theory (Fu et al, 2004;Miura, 1997;Xu et al, 2003). The solitary solutions, traveling wave solutions, quasi-periodic solutions and symmetries for the combined KdV-mKdV Eq.…”

Section: Introductionmentioning

confidence: 99%

New interaction solutions to the combined KdV–mKdV equation from CTE method

Tan

2016

Journal of the Association of Arab Universities for Basic and A

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The consistent tanh expansion (CTE) method is developed for the combined KdVmKdV equation. The combined KdV-mKdV equation is proved to be CTE solvable. New exact interaction solutions such as soliton-cnoidal wave solutions, soliton-periodic wave solutions for the combined KdV-mKdV equation are given out analytically and graphically. Ó 2016 The Authors. Production and hosting by Elsevier B.V. on behalf of University of Bahrain. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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New kinds of solutions to Gardner equation

Cited by 97 publications

References 16 publications

New solitons and kink solutions for the Gardner equation

New solitons and kink solutions for the Gardner equation

Some Coherent Excitations for the (2+1)-Dimensional Generalized Broer-Kaup System

New interaction solutions to the combined KdV–mKdV equation from CTE method

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