{"id":1851,"date":"2011-06-08T12:00:57","date_gmt":"2011-06-08T10:00:57","guid":{"rendered":"http:\/\/djalil.chafai.net\/blog\/?p=1851"},"modified":"2011-06-09T08:48:31","modified_gmt":"2011-06-09T06:48:31","slug":"some-famous-nonlinear-equations","status":"publish","type":"post","link":"https:\/\/djalil.chafai.net\/blog\/2011\/06\/08\/some-famous-nonlinear-equations\/","title":{"rendered":"Some famous nonlinear equations"},"content":{"rendered":"<p style=\"text-align: justify;\">Mathematicians and Physicists like to give fancy names to their favorite equations, such as <a title=\"The Monge-Amp\u00e8re equation appears in mass transportation problems\" href=\"http:\/\/en.wikipedia.org\/wiki\/Monge-Ampere_equation\">Monge-Amp\u00e8re<\/a>, <a title=\"The Hamilton-Jacobi equations appear in classical mechanics\" href=\"http:\/\/en.wikipedia.org\/wiki\/Hamilton%E2%80%93Jacobi_equation\">Hamilton-Jacobi<\/a>, <a title=\"The Navier-Stokes equations appear in fluid mechanics\" href=\"http:\/\/en.wikipedia.org\/wiki\/Navier-stokes\">Navier-Stokes<\/a>, <a title=\"The Cahn-Hilliard equation models phase separations\" href=\"http:\/\/en.wikipedia.org\/wiki\/Cahn%E2%80%93Hilliard_equation\">Cahn-Hilliard<\/a>, <a title=\"The Ginzburg-Landau equations appear in the modelling of superconductivity\" href=\"http:\/\/en.wikipedia.org\/wiki\/Ginzburg%E2%80%93Landau_theory\">Ginzburg-Landau<\/a>, etc. Do you know the definition and context of the following\u00a0 famous nonlinear partial differential equations of evolution?<\/p>\n<ul style=\"text-align: justify;\">\n<li><a title=\"NLS\" href=\"http:\/\/en.wikipedia.org\/wiki\/Nonlinear_Schr%C3%B6dinger_equation\">Non Linear Schr\u00f6dinger equation (NLS)<\/a><\/li>\n<li><a title=\"KdV\" href=\"http:\/\/en.wikipedia.org\/wiki\/Korteweg%E2%80%93de_Vries_equation\">Korteweg-de Vries equation (KdV)<\/a><\/li>\n<li><a title=\"Fisher-KPP\" href=\"http:\/\/en.wikipedia.org\/wiki\/Fisher%27s_equation\">Fisher-Kolmogorov-Petrovski-Piskunov equation (Fisher-KPP)<\/a><\/li>\n<li><a title=\"KPZ\" href=\"http:\/\/en.wikipedia.org\/wiki\/KPZ-Equation\">Kardar-Parisi-Zhang equation (KPZ)<\/a><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">The first two give rise to <a title=\"In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed.\" href=\"http:\/\/en.wikipedia.org\/wiki\/Soliton\">solitons<\/a>, the third one to traveling waves, while the last one is connected to interface growth and <a title=\"Tracy-Widom distributions\" href=\"\/blog\/2011\/05\/28\/tracy-widom\/\">Tracy-Widom<\/a> (<a title=\"The Kardar-Parisi-Zhang equation and universality class\" href=\"http:\/\/arxiv.org\/abs\/1106.1596\">survey<\/a>). You may find many other nonlinear equations with fancy names <a title=\"List of nonlinear partial differential equations\" href=\"http:\/\/en.wikipedia.org\/wiki\/List_of_nonlinear_partial_differential_equations\">here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mathematicians and Physicists like to give fancy names to their favorite equations, such as Monge-Amp&egrave;re, Hamilton-Jacobi, Navier-Stokes, Cahn-Hilliard, Ginzburg-Landau, etc. Do you know the definition&#8230;<\/p>\n<div class=\"more-link-wrapper\"><a class=\"more-link\" href=\"https:\/\/djalil.chafai.net\/blog\/2011\/06\/08\/some-famous-nonlinear-equations\/\">Continue reading<span class=\"screen-reader-text\">Some famous nonlinear equations<\/span><\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":583},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/1851"}],"collection":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/comments?post=1851"}],"version-history":[{"count":22,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/1851\/revisions"}],"predecessor-version":[{"id":1873,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/1851\/revisions\/1873"}],"wp:attachment":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/media?parent=1851"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/categories?post=1851"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/tags?post=1851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}