TY - JOUR

T1 - Construction of soliton equations using special polynomials

AU - Burde, G. I.

AU - Zarmi, Y.

PY - 2013/3/1

Y1 - 2013/3/1

N2 - A simple, algorithmic approach is proposed for the construction of the most general family of equations of a given scaling weight, possessing, at least, the same single-soliton solution as a given, lower scaling weight equation. The construction exploits special polynomials-differential polynomials in the solution, u, of an evolution equation, which vanish identically when u is a single-soliton solution. Applying the approach to different types of evolution equations yields new results concerning the most general families of evolution equations in a given scaling weight, which possess solitary wave solutions. The same method can be applied in the identification of families of evolution equations of mixed scaling weight (and, in general, of any structure), which admit single-soliton solutions of a desired form.

AB - A simple, algorithmic approach is proposed for the construction of the most general family of equations of a given scaling weight, possessing, at least, the same single-soliton solution as a given, lower scaling weight equation. The construction exploits special polynomials-differential polynomials in the solution, u, of an evolution equation, which vanish identically when u is a single-soliton solution. Applying the approach to different types of evolution equations yields new results concerning the most general families of evolution equations in a given scaling weight, which possess solitary wave solutions. The same method can be applied in the identification of families of evolution equations of mixed scaling weight (and, in general, of any structure), which admit single-soliton solutions of a desired form.

KW - Nonlinear evolution equations

KW - Soliton solutions

KW - Special polynomials

UR - http://www.scopus.com/inward/record.url?scp=84867471930&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2012.08.024

DO - 10.1016/j.cnsns.2012.08.024

M3 - Article

AN - SCOPUS:84867471930

VL - 18

SP - 519

EP - 527

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

IS - 3

ER -