Phase modulated domain walls and dark solitons for surface gravity waves

Highlights: • Localized solutions for dynamics of surface gravity waves at the critical point $kh\approx 1.363$. • The model admits domain walls and dark solitons with non-trivial phase. • Study the effect of wave parameters on the amplitude of surface gravity waves. We report theoretical prediction of localized solutions for dynamics of surface gravity waves, at the critical point $kh\approx 1.363$, modelled by higher-order nonlinear Schrödinger equation. The model possesses domain walls (kink solitons) and dark solitons modulated through different phase profiles. The parametric domains are delineated for the existence of soliton solutions. The effects of wave parameters have been discussed on the amplitude of surface gravity waves. Our work is motivated by Tsitoura et al. [1], on experimental and analytical observation of phase domain walls for deep water surface gravity waves modelled by nonlinear Schrödinger equation.