玻恩-英费尔德方程（Born-Infeld equation）是马克斯·玻恩和利奥波德·英费尔德创建的非线性偏微分方程[1]：
玻恩-英费尔德方程有许多行波解[2]
![{\displaystyle u[1]:=2*atan({\sqrt {(}}(a0+b1)/(a0-b1))*tan((1/2)*{\sqrt {(}}a0^{2}-b1^{2})*\eta ))+(1/2)*\pi }](//wikimedia.org/api/rest_v1/media/math/render/svg/d1b3c21c51e8c35c8a4cc4b6f93be6a3f5570539)
![{\displaystyle u[2]:=2*atan({\sqrt {(}}(a0+b1)/(a0-b1))*cot((1/2)*{\sqrt {(}}a0^{2}-b1^{2})*\eta ))+(1/2)*\pi }](//wikimedia.org/api/rest_v1/media/math/render/svg/ee3dbf39abbfc0c8119eea2ec25dbbcea32250ef)
![{\displaystyle u[3]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*tan((1/2)*{\sqrt {(}}a1^{2}+b1^{2})*\eta )/a1+b1/a1)}](//wikimedia.org/api/rest_v1/media/math/render/svg/4bcea0e8cc11c83a375e4da08690a9be905d1680)
![{\displaystyle u[4]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*cot((1/2)*{\sqrt {(}}a1^{2}+b1^{2})*\eta )/a1+b1/a1)}](//wikimedia.org/api/rest_v1/media/math/render/svg/ef7ce4c27b5d21ffc437fe4d3348e91d1ebc3795)
![{\displaystyle u[5]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*(coth({\sqrt {(}}a1^{2}+b1^{2})*eta)+csc({\sqrt {(}}a1^{2}+b1^{2})*eta))/a1+b1/a1)}](//wikimedia.org/api/rest_v1/media/math/render/svg/a5ee84a3e71d0a38b15fef0d10d91ce49aa38ae9)
![{\displaystyle u[6]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*(cosh({\sqrt {(}}a1^{2}+b1^{2})*\eta )+1)/(a1*sinh({\sqrt {(}}a1^{2}+b1^{2})*\eta ))+b1/a1)}](//wikimedia.org/api/rest_v1/media/math/render/svg/c329b55b006d512a270e0e245cbab9adfab79695)
![{\displaystyle u[7]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*sinh({\sqrt {(}}a1^{2}+b1^{2})*\eta )/(a1*(cosh({\sqrt {(}}a1^{2}+b1^{2})*\eta )+1))+b1/a1)}](//wikimedia.org/api/rest_v1/media/math/render/svg/faa803211570dc1ea385c48ed0c06fff3acfc827)
![{\displaystyle u[8]:=2*atan({\sqrt {(}}(a0+b1)/(b1-a0))*cot({\sqrt {(}}b1^{2}-a0^{2})*\eta +sec(h*{\sqrt {(}}b1^{2}-a0^{2})*\eta )))+(1/2)*\pi }](//wikimedia.org/api/rest_v1/media/math/render/svg/d22373218e3ce85d09d507baba7633ec393d41ff)
![{\displaystyle u[9]:=2*atan({\sqrt {(}}(a0+b1)/(b1-a0))*sinh({\sqrt {(}}b1^{2}-a0^{2})*\eta )/(cosh({\sqrt {(}}b1^{2}-a0^{2})*eta)+1))}](//wikimedia.org/api/rest_v1/media/math/render/svg/a4b316d7797e0b51c91d7b5d670ebfc76cf2052f)
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![{\displaystyle u[1]:=2*atan({\sqrt {(}}(a0+b1)/(a0-b1))*tan((1/2)*{\sqrt {(}}a0^{2}-b1^{2})*\eta ))+(1/2)*\pi }](http://wikimedia.org/api/rest_v1/media/math/render/svg/d1b3c21c51e8c35c8a4cc4b6f93be6a3f5570539)
![{\displaystyle u[2]:=2*atan({\sqrt {(}}(a0+b1)/(a0-b1))*cot((1/2)*{\sqrt {(}}a0^{2}-b1^{2})*\eta ))+(1/2)*\pi }](http://wikimedia.org/api/rest_v1/media/math/render/svg/ee3dbf39abbfc0c8119eea2ec25dbbcea32250ef)
![{\displaystyle u[3]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*tan((1/2)*{\sqrt {(}}a1^{2}+b1^{2})*\eta )/a1+b1/a1)}](http://wikimedia.org/api/rest_v1/media/math/render/svg/4bcea0e8cc11c83a375e4da08690a9be905d1680)
![{\displaystyle u[4]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*cot((1/2)*{\sqrt {(}}a1^{2}+b1^{2})*\eta )/a1+b1/a1)}](http://wikimedia.org/api/rest_v1/media/math/render/svg/ef7ce4c27b5d21ffc437fe4d3348e91d1ebc3795)
![{\displaystyle u[5]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*(coth({\sqrt {(}}a1^{2}+b1^{2})*eta)+csc({\sqrt {(}}a1^{2}+b1^{2})*eta))/a1+b1/a1)}](http://wikimedia.org/api/rest_v1/media/math/render/svg/a5ee84a3e71d0a38b15fef0d10d91ce49aa38ae9)
![{\displaystyle u[6]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*(cosh({\sqrt {(}}a1^{2}+b1^{2})*\eta )+1)/(a1*sinh({\sqrt {(}}a1^{2}+b1^{2})*\eta ))+b1/a1)}](http://wikimedia.org/api/rest_v1/media/math/render/svg/c329b55b006d512a270e0e245cbab9adfab79695)
![{\displaystyle u[7]:=2*atan({\sqrt {(}}a1^{2}+b1^{2})*sinh({\sqrt {(}}a1^{2}+b1^{2})*\eta )/(a1*(cosh({\sqrt {(}}a1^{2}+b1^{2})*\eta )+1))+b1/a1)}](http://wikimedia.org/api/rest_v1/media/math/render/svg/faa803211570dc1ea385c48ed0c06fff3acfc827)
![{\displaystyle u[8]:=2*atan({\sqrt {(}}(a0+b1)/(b1-a0))*cot({\sqrt {(}}b1^{2}-a0^{2})*\eta +sec(h*{\sqrt {(}}b1^{2}-a0^{2})*\eta )))+(1/2)*\pi }](http://wikimedia.org/api/rest_v1/media/math/render/svg/d22373218e3ce85d09d507baba7633ec393d41ff)
![{\displaystyle u[9]:=2*atan({\sqrt {(}}(a0+b1)/(b1-a0))*sinh({\sqrt {(}}b1^{2}-a0^{2})*\eta )/(cosh({\sqrt {(}}b1^{2}-a0^{2})*eta)+1))}](http://wikimedia.org/api/rest_v1/media/math/render/svg/a4b316d7797e0b51c91d7b5d670ebfc76cf2052f)
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