Search results for "mKdV equation"
showing 4 items of 4 documents
From particular polynomials to rational solutions to the mKdV equation
2022
Rational solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of determinants involving certain particular polynomials. This gives a very efficient method to construct solutions. We construct very easily explicit expressions of these rational solutions for the first orders n = 1 until 10.
Multi-parameters rational solutions to the mKdV equation
2021
N-order solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6.
Rational solutions to the mKdV equation associated to particular polynomials
2021
International audience; Rational solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of determinants involving certain particular polynomials. This gives a very efficient method to construct solutions. We construct very easily explicit expressions of these rational solutions for the first orders n = 1 until 10.
The mKdV equation and multi-parameters rational solutions
2021
Abstract N -order solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2 N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2 N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6 .