A new integrable equation that combines the KdV equation with the negative-order KdV equation

作者：Wazwaz Abdul-Majid^*

来源：Mathematical Methods in the Applied Sciences, 2018, 41(1): 80-87.

DOI：10.1002/mma.4595

• KdV equation
• negative-order KdV equation
• recursion operator
• multiple soliton solutions
• Painleve analysis

In this work, we develop a new integrable equation by combining the KdV equation and the negative-order KdV equation. We use concurrently the KdV recursion operator and the inverse KdV recursion operator to construct this new integrable equation. We show that this equation nicely passes the Painleve test. As a result, multiple soliton solutions and other soliton and periodic solutions are guaranteed and formally derived.

• 出版日期2018-1-15