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Yang, Hongwei; Wang, Xiangrong; Yin, Baoshu

On differential equations derived from the pseudospherical surfaces. (English) Zbl 1472.35343

Abstr. Appl. Anal. 2014, Article ID 381717, 9 p. (2014).
Summary: We construct two metric tensor fields; by means of these metric tensor fields, sinh-Gordon equation and elliptic sinh-Gordon equation are obtained, which describe pseudospherical surfaces of constant negative Riemann curvature scalar \(\sigma\) = \(-\)2, \(\sigma\) = \(-\)1, respectively. By employing the Bäcklund transformation, nonlinear superposition formulas of sinh-Gordon equation and elliptic sinh-Gordon equation are derived; various new exact solutions of the equations are obtained.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35L71 Second-order semilinear hyperbolic equations
15A69 Multilinear algebra, tensor calculus

Keywords:

sinh-Gordon equation; elliptic sinh-Gordon equation; Bäcklund transformation; tensor fields
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\textit{H. Yang} et al., Abstr. Appl. Anal. 2014, Article ID 381717, 9 p. (2014; Zbl 1472.35343)
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References:

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