A hierarchy of new nonlinear evolution equations and generalized bi-Hamiltonian structures

Wei, Jiao; Geng, Xianguo

doi:10.1016/j.amc.2015.06.105

Cited by 8 publications

(3 citation statements)

References 22 publications

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“…In succession, the maximum amplitude of u [1] is −(e 2 0 − 3µ 2 )u 0 /(e 2 0 + µ 2 ) and the critical line is defined by Eq. (38), see Fig. 4(d).…”

Section: Rational Solutionsmentioning

confidence: 94%

“…The maximum value of w [1] is (3e 2 0 − µ 2 )µu 0 /e 0 (e 2 0 + µ 2 ) and the critical line is defined by Eq. (38). While the minimum value of w [1] is −(3e 2 0 + 2µ 2 )µu 0 /2e 0 (e 2 0 + µ 2 ) and is reached at…”

Section: Rational Solutionsmentioning

confidence: 95%

“…For our studies, we begin with the Lax pair of Eq. (1) which can be given through the Ablowitz-Kaup-Newell-Segur (AKNS) technique [37][38][39][40]:…”

Section: Periodic Solutionsmentioning

confidence: 99%

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Periodic and rational solutions of the reduced Maxwell–Bloch equations

Wei

Wang

Geng

2018

Communications in Nonlinear Science and Numerical Simulation

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We investigate the reduced Maxwell-Bloch (RMB) equations which describe the propagation of short optical pulses in dielectric materials with resonant non-degenerate transitions. The general Nth-order periodic solutions are provided by means of the Darboux transformation, and from two different limiting cases of the obtained general periodic solutions, the Nth-order degenerate periodic and Nth-order rational solutions containing several free parameters with compact determinant representations are derived, respectively. Explicit expressions of these solutions from first to second order are presented. Typical nonlinear wave patterns for the four components of the RMB equations such as single-peak, double-peak-double-dip, double-peak and single-dip structures in the second-order rational solutions are shown. This kind of the rational solutions correspond to rogue waves in the reduced Maxwell-Bloch equations.

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“…In succession, the maximum amplitude of u [1] is −(e 2 0 − 3µ 2 )u 0 /(e 2 0 + µ 2 ) and the critical line is defined by Eq. (38), see Fig. 4(d).…”

Section: Rational Solutionsmentioning

confidence: 94%