<span class="mw-page-title-main">Soliton</span>

Soliton

<p>In <a href="/en/Mathematics" title="Mathematics" class="wl">mathematics</a> and <a href="/en/Physics" title="Physics" class="wl">physics</a>, a <b>soliton</b> or <b>solitary wave</b> is a self-reinforcing <a href="/en/Wave_packet" title="Wave packet" class="wl">wave packet</a> that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of <a href="/en/Nonlinearity" title="Nonlinearity" class="mw-redirect wl">nonlinear</a> and <a href="/en/Dispersion_relation" title="Dispersion relation" class="wl">dispersive effects</a> in the medium. (Dispersive effects are a property of certain systems where the speed of a wave depends on its frequency.) Solitons are the solutions of a widespread class of weakly nonlinear dispersive <a href="/en/Partial_differential_equation" title="Partial differential equation" class="wl">partial differential equations</a> describing physical systems.</p>

<style data-mw-deduplicate="TemplateStyles:r1033289096" typeof="mw:Extension/templatestyles mw:Transclusion">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style>
<div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none" about="#mwt4">Self-reinforcing single wave packet</div>
<figure class="wiki-thumb"><a href="/en/File:Soliton_hydro.jpg" class="mw-file-description image media-thumb" data-hash="File:Soliton_hydro.jpg"><img loading="lazy" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Soliton_hydro.jpg/250px-Soliton_hydro.jpg" decoding="async" data-file-width="600" data-file-height="285" data-file-type="bitmap" height="119" width="250" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Soliton_hydro.jpg/375px-Soliton_hydro.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Soliton_hydro.jpg/500px-Soliton_hydro.jpg 2x" alt="Soliton_hydro.jpg"></a><figcaption><a href="/en/Solitary_wave_(water_waves)" title="Solitary wave (water waves)" class="mw-redirect wl">Solitary wave</a> in a laboratory <a href="/en/Wave_channel" title="Wave channel" class="mw-redirect wl">wave channel</a></figcaption></figure>
<p>The soliton phenomenon was first described in 1834 by <a href="/en/John_Russell_(engineer)" title="John Russell (engineer)" class="mw-redirect wl">John Scott Russell</a> (1808–1882) who observed a solitary wave in the <a href="/en/Union_Canal_(Scotland)" title="Union Canal (Scotland)" class="wl">Union Canal</a> in Scotland. He reproduced the phenomenon in a <a href="/en/Wave_tank" title="Wave tank" class="wl">wave tank</a> and named it the "<a href="/en/John_Russell_(engineer)#The_wave_of_translation" title="John Russell (engineer)" class="mw-redirect wl">Wave of Translation</a>".</p>



In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. Solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described in 1834 by John Scott Russell who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation". 