Conservation laws, traveling wave solutions and wavelet solution for the two-component Novikov equation

Abstract The objective of this present article is to study the two-component Novikov equation. This equation is also known as Geng–Xue equation and is characterized by cubic nonlinearities. By applying the multiplier method, new conserved quantities are found, and some traveling wave solutions are derived based on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mfrac> <mml:msup> <mml:mi>G</mml:mi> <mml:mrow> <mml:mi>′</mml:mi> </mml:mrow> </mml:msup> <mml:mi>G</mml:mi> </mml:mfrac> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> -expansion method. Furthermore, a numerical solution is determined by employing the Haar wavelet collocation (HWC) method. In order to confirm the accuracy, this numerical solution is compared with the solution obtained by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mfrac> <mml:msup> <mml:mi>G</mml:mi> <mml:mrow> <mml:mi>′</mml:mi> </mml:mrow> </mml:msup> <mml:mi>G</mml:mi> </mml:mfrac> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> -expansion method. Additionally, the convergence analysis of the HWC method is also presented.