Non-linear electrostatic waves in pair-ion plasmas - National Centre ...
Non-linear electrostatic waves in pair-ion plasmas - National Centre ...
Non-linear electrostatic waves in pair-ion plasmas - National Centre ...
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1. Soliton‣ Soliton is a non<strong>l<strong>in</strong>ear</strong> structure (bell shaped) which conserves itsshape and <strong>in</strong>teracts with surround<strong>in</strong>gs or other solitons as an<strong>in</strong>dependent particle.‣ Solitons are robust aga<strong>in</strong>st perturbat<strong>ion</strong>s.‣ Soliton was first noticed <strong>in</strong> the month of August 1834 by the Scottisheng<strong>in</strong>eer John Scott Russell (1808-1882), while conduct<strong>in</strong>gexperiments to determ<strong>in</strong>e the most efficient design for canal boatsalong the Un<strong>ion</strong> canal l<strong>in</strong>k<strong>in</strong>g Ed<strong>in</strong>burg with Glasgow.‣ In 1885, Korteweg and de Vries derived a model equat<strong>ion</strong> (knownas KdV equat<strong>ion</strong>) for the dynamics of non<strong>l<strong>in</strong>ear</strong> wave as follows,3∂u∂u∂ u+ au + b3∂t∂x∂x= 0Here a and b are non zero constants, which depends on fluid properties.The KdV equat<strong>ion</strong> posses a soliton (or solitray wave) solut<strong>ion</strong>.3
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