霍赫洛夫-沯波咯慈卡娅方程( Khokhlov--Zabolotskaya equation)是一个非线性偏微分方程：

u_{xx}+[(\alphau+\beta)u_{y}]_{y}=0

解析解
霍赫洛夫-沯波咯慈卡娅方程有行波解：
:p[2] := 1.32+1.4934776966447732662(1.56+1.7969454312181156991x^1.2+1.2C[2]^1.2y^1.2)^1.2
:p[3] := 1.32+1.4934776966447732662(.2707963267948966192-1.4974545260150964159x^1.2-1.C[2]^1.2y^1.2)^1.2
:p[7] := 1.32+1.4934776966447732662((55.009468881881296225-14.965237496723309046I)sqrt(1.-.
:66321499013806706114JacobiNS(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2-(.38969456396968710805I)JacobiNS(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2)sqrt(1.-.66321499013806706114JacobiNS(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2+(.38969456396968710805I)JacobiNS(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2)EllipticF((.84629952125971224961+.23023442302651244686I)JacobiNS(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3), .86217948717948717949-.50660293316059324046I)/sqrt(3000.JacobiNS(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^4-6725.JacobiNS(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2+5070.))^1.2

:p[8] := 1.32+1.4934776966447732662(-(34.214441730088728277I)sqrt(1.+2.1356058039711429821JacobiDN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2)sqrt(1.-2.2476058039711429821JacobiDN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2)EllipticF((1.4613712067681992557I)JacobiDN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3), 1.0258869993454412308I)/sqrt(3000.JacobiDN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^4+70.JacobiDN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2*y^1.2, 1.3)^2-625.))^1.2

:p[9] := 1.32+1.4934776966447732662((38.347855408516105018-11.263642905975212858I)sqrt(1.-1.3164251207729468599JacobiCN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2-(.84634523908200302082I)JacobiCN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2)sqrt(1.-1.3164251207729468599JacobiCN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2+(.84634523908200302082I)JacobiCN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^2)EllipticF((1.2003002147146243158+.35255564762321759608I)JacobiCN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3), .84115756322748992840-.54079011994043611908I)/sqrt(5070.JacobiCN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2y^1.2, 1.3)^4-5450.JacobiCN(1.68+1.9520491881558575047x^1.2+1.2C[2]^1.2*y^1.2, 1.3)^2+2070.))^1.2
p[10] := 1.32+1.4934776966447732662arctan(1/sqrt(1.2csc(1.56+1.7969454312181156991x^1.2+1.2C[2]^1.2*y^1.2)^2-1.2))^1.2
:p[11] := 1.32+1.4934776966447732662arctan(1/sqrt(1.2sec(1.56+1.7969454312181156991x^1.2+1.2C[2]^1.2*y^1.2)^2-1.2))^1.2
:p[12] := 1.32+1.4934776966447732662arctan(1/sqrt(1.2sech(1.56+1.7969454312181156991x^1.2+1.2C[2]^1.2*y^1.2)^2-1.2))^1.2
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