Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schrödinger flow

In a previous work El et al. (2006) exact stable oblique soliton solutions were revealed in two-dimensional nonlinear Schrödinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt to build two-soliton solutions shows that the system is "close" to integrability provided that the angle between the solitons is small and/or we are in the hypersonic limit. -- Highlights: ► We express single soliton solution within the Hirota bilinear formalism. ► We investigate two-soliton solutions. ► The system is close to integrability provided that we are in the hypersonic limit. ► It is close to integrability provided that the angle between solitons is small.