Lax pair

Lax pair

In <a href="/en/Mathematics" title="Mathematics" class="wl">mathematics</a>, in the theory of <a href="/en/Integrable_systems" title="Integrable systems" class="mw-redirect wl">integrable systems</a>, a Lax pair is a pair of time-dependent matrices or <a href="/en/Operator_(mathematics)" title="Operator (mathematics)" class="wl">operators</a> that satisfy a corresponding <a href="/en/Differential_equation" title="Differential equation" class="wl">differential equation</a>, called the Lax equation. Lax pairs were introduced by <a href="/en/Peter_Lax" title="Peter Lax" class="wl">Peter Lax</a> to discuss <a href="/en/Soliton" title="Soliton" class="wl">solitons</a> in <a href="/en/Continuous_media" title="Continuous media" class="mw-redirect wl">continuous media</a>. The <a href="/en/Inverse_scattering_transform" title="Inverse scattering transform" class="wl">inverse scattering transform</a> makes use of the Lax equations to solve such systems.

In mathematics, in the theory of integrable systems, a Lax pair is a pair of time-dependent matrices or operators that satisfy a corresponding differential equation, called the Lax equation. Lax pairs were introduced by Peter Lax to discuss solitons in continuous media. The inverse scattering transform makes use of the Lax equations to solve such systems. 