Solitons and other solutions to the quantum Zakharov-Kuznetsov equation

Abstract

In this paper, we present G′/G-expansion method, exp-function method, modified F-expansion method as well as the traveling wave hypothesis for finding the exact traveling wave solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas. By these methods, rich families of exact solutions have been obtained, including soliton solutions. This work continues to reinforce the idea that the proposed methods, with the help of symbolic computation, provide a powerful mathematical tool for solving nonlinear partial differential equations.

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Correspondence to Anjan Biswas.

Appendix

Appendix

Relations between values of A, B, C and corresponding F(ξ) in Riccati equation:

$$F'(\xi)=A+BF(\xi)+CF^2(\xi)$$
A B C F
0 1 −1 \(\frac{1}{2}+\frac{1}{2}\tanh(\frac{1}{2}\xi)\)
0 −1 1 \(\frac{1}{2}-\frac{1}{2}\mathop{\mathrm{coth}}(\frac{1}{2}\xi)\)
\(\frac{1}{2}\) 0 \(-\frac{1}{2}\)  coth(ξ)± csch(ξ), tanh(ξi sech(ξ)
1 0 −1 tanh(ξ), coth(ξ)
\(\frac{1}{2}\) 0 \(\frac{1}{2}\) sec(ξ)+tan(ξ), csc(ξ)−cot(ξ)
\(-\frac{1}{2}\) 0 -\(\frac{1}{2}\) sec(ξ)−tan(ξ), csc(ξ)+cot(ξ)
1(−1) 0 1(−1) tanξcotξ
0 0 ≠0 \(-\frac{1}{C\xi+\lambda}\) (λ is an arbitrary constant)

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Ebadi, G., Mojaver, A., Milovic, D. et al. Solitons and other solutions to the quantum Zakharov-Kuznetsov equation. Astrophys Space Sci 341, 507–513 (2012). https://doi.org/10.1007/s10509-012-1072-z

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Keywords

  • Solitons
  • Quantum Zakharov-Kuznetsov equation
  • Traveling waves