MULTIPLE SOLITON SOLUTIONS FOR TWO INTEGRABLE COUPLINGS OF THE MODIFIED KORTEWEG-DE VRIES EQUATION

作者：Wazwaz Abdul Majid^*

来源：Proceedings of the Romanian Academy - Series A: Mathematics, Physics, Technical Sciences, Information Science , 2013, 14(3): 219-225.

• integrable couplings
• backlund transformations
• modified Korteweg-de Vries equation
• multiple soliton solutions

In this work, we use the algebra of coupled scalars to develop two kinds of nonlinear integrable couplings of the modified Korteweg-de Vries (mKdV) equation. One of the integrable couplings of the mKdV equation gives multiple soliton solutions of distinct amplitudes, whereas the second kind gives multiple singular soliton solutions of distinct amplitudes as well. The Backlund transformation and the simplified Hirota's method will be used for this study. We show that these couplings possess multiple soliton solutions the same as the multiple soliton solutions of the mKdV equation, but differ only in the coefficients of the Backlund transformation. This difference exhibits soliton solutions with distinct amplitudes.

• 出版日期2013-9