Abstract
Based on the symbolic computation, a class of lump solutions to the (2+1)-dimensional Sawada-Kotera (2DSK) equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.
Highlights
In soliton theories [1,2,3,4,5,6,7,8], as a special kind of rational solution, rogue wave has been published in different fields since Solli et al first reported the existence of optical rogue wave in 2007 [9]
Through Hirota bilinear form and symbolic calculation, we investigate the (2+1)-dimensional Sawada-Kotera equation
Its lump solutions are provided first, and the analyticity and localization of the resulting solutions are guaranteed by two determinant conditions
Summary
In soliton theories [1,2,3,4,5,6,7,8], as a special kind of rational solution, rogue wave has been published in different fields since Solli et al first reported the existence of optical rogue wave in 2007 [9]. Where f is positive; with this transformation, we obtain the following Hirota bilinear form of 2DSK equation:. In order to guarantee that f is positive, it needs a9 > 0; the parameters need to satisfy these conditions These sets lead to guarantee of the well-defined function f and a class of positive quadratic function solutions to the bilinear 2DSK equation in (4): f [a1x a2y.
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