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Numerical investigation on the 3-periodic wave solutions of (1+1)-dimensional and (2+1)-dimensional integrable equations

Author

Listed:
  • Gong, Yutao
  • Wang, Yunhu
  • Dong, Huanhe

Abstract

The direct method proposed by Akira Nakamura for finding N-periodic wave solutions yields quick results for N=1 and 2. However, when N≥3, the difficulty in solving over-determined systems makes it challenging to further obtain the periodic solutions of the equations. This paper combines the Gauss–Newton method with Akira Nakamura’s direct method to calculate 3-periodic wave solutions to four (1+1)-dimensional and (2+1)-dimensional integrable equations: the combined KdV–Caudrey–Dodd–Gibbon equation, the (2+1)-dimensional KdV equation, the (2+1)-dimensional Ito equation and the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation. Detailed numerical experiments are conducted to demonstrate the existence of 3-periodic wave solutions.

Suggested Citation

  • Gong, Yutao & Wang, Yunhu & Dong, Huanhe, 2025. "Numerical investigation on the 3-periodic wave solutions of (1+1)-dimensional and (2+1)-dimensional integrable equations," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006228
    DOI: 10.1016/j.chaos.2025.116609
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