波格雅夫连斯基-科譳普勒琛科方程（Bogoyavlenski-Konoplechenko equation）是一个二元非线性偏微分方程

u_{xt}+\alphau_{xxxx}+\betau_{xxxy}+6\alphau_{xx}u_{x}+4\betau_{xy}u_{x}+\betau_{xx}u_{y}=0

解析解
行波解
u(x, y, t) = _C5+_C6cos(_C1+_C2x-(3/4)_C2y/\beta+(1/4)_C2^3t)
u(x, y, t) = _C5+_C6sinh(_C1+_C2x-(3/4)_C2y/\beta-(1/4)_C2^3t)
u(x, y, t) = _C5+_C7cosh(_C1+_C2x-(3/4)_C2y/\beta-_C2^3*t)^2
u(x, y, t) = _C5+6_C2(\beta_C3+_C2)cot(_C1+_C2x+_C3y+(4_C2^3+4\beta_C3_C2^2)t)/(3_C2+4\beta_C3)
u(x, y, t) = _C5-(3/4)_C8cosh(_C1+_C2x-(3/4)_C2y/\beta-(9/4)_C2^3t)+_C8cosh(_C1+_C2x-(3/4)_C2y/\beta-(9/4)_C2^3*t)^3
u(x, y, t) = _C6-_C10cosh(_C2+_C3x-(3/4)_C3y/\beta-4_C3^3t)^2+_C10cosh(_C2+_C3x-(3/4)_C3y/\beta-4_C3^3t)^4
u(x, y, t) = _C6+(5/16)_C11cosh(_C2+_C3x-(3/4)_C3y/\beta-(25/4)_C3^3t)-(5/4)_C11cosh(_C2+_C3x-(3/4)_C3y/\beta-(25/4)_C3^3t)^3+_C11cosh(_C2+_C3x-(3/4)_C3y/\beta-(25/4)_C3^3t)^5
行波图
参考文献

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