Soliton resolution and large time behavior of solutions to the Cauchy problem for the Novikov equation with a nonzero background

The Sasa–Satsuma equation with high-order discrete spectra in space-time solitonic regions: soliton resolution via the mixed ∂ ¯ Zhang, Yan 2024Commun. Theor. Phys.0000View full textAdd to dashboardCite

“…As a development of the Deift-Zhou nonlinear steepest descent method, a powerful tool called the ¶-steepest descent method was first proposed by Mclaughlin and miller to analyze the asymptotic behaviors of orthogonal polynomials [10,11]. Later, this method was successfully used to analyze the long-time behaviors of solutions to integrable nonlinear wave equations, such as the focusing NLS equation [12,13], the defocusing NLS equation [14,15], the derivative NLS equation [16], the mKdV equation [17,18], the fifth-order mKdV equation [19], the complex short pulse equation [20], the modified Camassa-Holm equation [21], the Novikov equation [22], etc.…”

Data-driven fusion and fission solutions in the Hirota–Satsuma–Ito equation via the physics-informed neural networks method

“…Therefore, many scholars have investigated thesoliton solutions of nonlinear systems and a number of interesting results have been achieved. For example, Fan's group discussed the soliton resolution and large-time behavior of solutions to the Cauchy problem for the Novikov equation [22]. Yan's group analyzed soliton formation and its dynamicbehaviors in quintic nonlinear media [23].…”