| Citation: |
Junliang Lu, Xiaochun Hong, Qi Zhao. NEW EXACT SOLUTIONS FOR COUPLED SCHRÖDINGER-BOUSSINESQ EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 741-765. doi: 10.11948/20190380
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NEW EXACT SOLUTIONS FOR COUPLED SCHRÖDINGER-BOUSSINESQ EQUATIONS
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Abstract
Due to the importance of the coupled Schrödinger-Boussinesq equations (CSBEs) in applied physics, many mathematicians and physicists are interesting to CSBEs. One of the main tasks of studying CSBEs is to obtain the exact solutions for CSBEs. In this paper, we firstly use the coupled Riccati equations to change the polynomial expansion method. Secondly, CSBEs are changed into coupled ordinary differential equations by the traveling wave solution transformation. Then, we assume that the solutions for the coupled ordinary differential equations satisfy the coupled Riccati equations and substitute the solutions of the coupled Riccati equations into the coupled ordinary differential equations. By calculating the algebra system, we successfully construct more new exact traveling wave solutions for CSBEs with distinct physical structures. The exact solutions with arbitrary parameters are expressed by sech, sech2, tanh, sinh, cosh, et al, functions, respectively. When the parameters are taken as special values, some examples are given to demonstrate the solutions and their physical meaning.
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References
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Junliang Lu, Xiaochun Hong, Qi Zhao. NEW EXACT SOLUTIONS FOR COUPLED SCHRÖDINGER-BOUSSINESQ EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 741-765. doi: 10.11948/20190380
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Figure 1. The real part of the solution
$ u_1(x, t) $ as shown in (a), the imaginary part of the solution$ u_1(x, t) $ as shown in (b), the norm of the solution$ u_1(x, t) $ as shown in (c), and the solution$ v_1(x, t) $ as shown in (d). -
Figure 2. The real part of the solution
$ u_4(x, t) $ as shown in (a), the imaginary part of the solution$ u_4(x, t) $ as shown in (b), the norm of the solution$ u_4(x, t) $ as shown in (c), and the solution$ v_4(x, t) $ as shown in (d). -
Figure 3. The real part of the solution
$ u_9(x, t) $ as shown in (a), the imaginary part of the solution$ u_9(x, t) $ as shown in (b), the norm of the solution$ u_9(x, t) $ as shown in (c), and the solution$ v_9(x, t) $ as shown in (d).