Breather molecules and localized interaction solutions in the (2+1)-dimensional BLMP equation

Jiaxin Qi,Hongli An,Peng Jin

Table 1. Breather-soliton molecule and interaction solutions.

N = 3 + P Name of the solution Restriction conditions P = 0 {BSM} ${k}_{1}={k}_{2}^{* }={k}_{1r}+{\rm{i}}{k}_{1i},\quad {p}_{1}={p}_{2}^{* }\,=\,{p}_{1r}+{\rm{i}}{p}_{1i}$, $\tfrac{{k}_{1r}}{{k}_{3}}=\tfrac{{k}_{1r}\ {p}_{1r}-{k}_{1i}\ {p}_{1i}}{{k}_{3}\ {p}_{3}}=\tfrac{{k}_{1r}^{3}-3{k}_{1r}\ {k}_{1i}^{2}}{{k}_{3}^{3}}$ P = 1 {BSM, S} the same as above P = 2 {BSM, B} ${k}_{1}={k}_{2}^{* }={k}_{1r}+{\rm{i}}{k}_{1i},\quad {p}_{1}={p}_{2}^{* }\,=\,{p}_{1r}+{\rm{i}}{p}_{1i}$, ${k}_{4}={k}_{5}^{* }={k}_{4r}+{\rm{i}}{k}_{4i},\quad {p}_{4}={p}_{5}^{* }={p}_{4r}+{\rm{i}}{p}_{4i}$ $\tfrac{{k}_{1r}}{{k}_{3}}=\tfrac{{k}_{1r}\ {p}_{1r}-{k}_{1i}\ {p}_{1i}}{{k}_{3}\ {p}_{3}}=\tfrac{{k}_{1r}^{3}-3{k}_{1r}\ {k}_{1i}^{2}}{{k}_{3}^{3}}$, P = 2 {BSM, L} ${k}_{1}={k}_{2}^{* }={k}_{1r}+{\rm{i}}{k}_{1i},\quad {p}_{1}={p}_{2}^{* }\,=\,{p}_{1r}+{\rm{i}}{p}_{1i}$, ${k}_{4}={k}_{5}^{* }={k}_{4r}+{\rm{i}}{k}_{4i},\quad {p}_{4}={p}_{5}^{* }={p}_{4r}+{\rm{i}}{p}_{4i}$, $\tfrac{{k}_{1r}}{{k}_{3}}=\tfrac{{k}_{1r}\ {p}_{1r}-{k}_{1i}\ {p}_{1i}}{{k}_{3}\ {p}_{3}}=\tfrac{{k}_{1r}^{3}-3{k}_{1r}\ {k}_{1i}^{2}}{{k}_{3}^{3}}$, ${k}_{4r}^{2}+{k}_{4i}^{2}\to 0$ P = 3 {BSM, B, S} the same as what's used in {BSM, B} P = 3 {BSM, L, S} the same as what's used in {BSM, L} P = 3 {BSM, BSM} ${k}_{1}={k}_{2}^{* }={k}_{1r}+{\rm{i}}{k}_{1i},\quad {p}_{1}={p}_{2}^{* }\,=\,{p}_{1r}+{\rm{i}}{p}_{1i}$, ${k}_{4}={k}_{5}^{* }={k}_{4r}+{\rm{i}}{k}_{4i},\quad {p}_{4}={p}_{5}^{* }\,=\,{p}_{4r}+{\rm{i}}{p}_{4i}$, $\tfrac{{k}_{1r}}{{k}_{3}}=\tfrac{{k}_{1r}\ {p}_{1r}-{k}_{1i}\ {p}_{1i}}{{k}_{3}\ {p}_{3}}=\tfrac{{k}_{1r}^{3}-3{k}_{1r}\ {k}_{1i}^{2}}\ {{k}_{3}^{3}}$, $\tfrac{{k}_{4r}}{{k}_{6}}=\tfrac{{k}_{4r}\ {p}_{4r}-{k}_{4i}\ {p}_{4i}}{{k}_{6}\ {p}_{6}}=\tfrac{{k}_{4r}^{3}-3{k}_{4r}\ {k}_{4i}^{2}}{{k}_{6}^{3}}$