Loading [MathJax]/jax/output/HTML-CSS/jax.js

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

Jiaxin Qi,Hongli An,Peng Jin

Table 2. Breather molecule and interaction solutions.

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