Conservation Laws of Some Physical Models via Symbolic Package GeM

Table 1

Multipliers and conserved vectors for PDE (14).

Multiplier	Fluxes
Λ^(1)=𝑢𝑡	𝜙^(1)=𝜆^2+12𝑢𝑢𝑥𝑥+12𝑢𝑢𝑧𝑧−12𝑢^2𝑡−𝜆^2cosh𝑢
	𝜓^(1)1=−2𝑢𝑢𝑡𝑥+12𝑢𝑡𝑢𝑥
	𝜋^(1)1=−2𝑢𝑢𝑡𝑧+12𝑢𝑡𝑢𝑧
Λ^(2)=𝑢𝑥	𝜙^(2)=12𝑢𝑢𝑡𝑥−12𝑢𝑡𝑢𝑥
	𝜓^(2)=𝜆^2+12𝑢𝑢𝑧𝑧+12𝑢^2𝑥−𝜆^21cosh𝑢−2𝑢𝑢𝑡𝑡
	𝜋^(2)1=−2𝑢𝑢𝑥𝑧+12𝑢𝑥𝑢𝑧
Λ^(3)=𝑢𝑧	𝜙^(3)=12𝑢𝑢𝑡𝑧−12𝑢𝑡𝑢𝑧
	𝜓^(3)1=−2𝑢𝑢𝑥𝑧+12𝑢𝑥𝑢𝑧
	𝜋^(3)=𝜆^2+12𝑢𝑢𝑥𝑥+12𝑢^2𝑧−𝜆^21cosh𝑢−2𝑢𝑢𝑡𝑡
Λ^(4)=𝑥𝑢𝑡+𝑡𝑢𝑥	𝜙^(4)=12𝑢𝑢𝑥−12𝑥𝑢^2𝑡+12𝑡𝑢𝑢𝑡𝑥−12𝑡𝑢𝑡𝑢𝑥+12𝑥𝑢𝑢𝑧𝑧+12𝑥𝑢𝑢𝑥𝑥−𝜆^2𝑥cosh𝑢+𝜆^2𝑥
	𝜓^(4)1=−2𝑥𝑢𝑢𝑡𝑥−12𝑡𝑢𝑢𝑡𝑡+12𝑥𝑢𝑥𝑢𝑡+12𝑡𝑢𝑢𝑧𝑧+𝜆^2𝑡−𝜆^21𝑡cosh𝑢−2𝑢𝑢𝑡+12𝑡𝑢^2𝑥
	𝜋^(4)1=−2𝑥𝑢𝑢𝑡𝑧+12𝑥𝑢𝑡𝑢𝑧−12𝑡𝑢𝑢𝑥𝑧+12𝑡𝑢𝑥𝑢𝑧
Λ^(5)=−𝑧𝑢𝑥+𝑥𝑢𝑧	𝜙^(5)=12𝑧𝑢𝑢𝑡𝑥+12𝑥𝑢𝑢𝑡𝑧+12𝑧𝑢𝑡𝑢𝑥−12𝑥𝑢𝑡𝑢𝑧
	𝜓^(5)1=−2𝑢𝑢𝑧−12𝑧𝑢𝑢𝑧𝑧−12𝑥𝑢𝑢𝑥𝑧+12𝑧𝑢𝑢𝑡𝑡−12𝑧𝑢^2𝑥+12𝑥𝑢𝑥𝑢𝑧−𝜆^2𝑧+𝜆^2𝑧cosh𝑢
	𝜋^(5)=12𝑢𝑢𝑥+12𝑥𝑢𝑢𝑥𝑥−𝜆^21𝑥cosh𝑢+2𝑥𝑢^2𝑧+12𝑧𝑢𝑢𝑥𝑧−12𝑧𝑢𝑧𝑢𝑥−12𝑥𝑢𝑢𝑡𝑡+𝜆^2𝑥
Λ^(6)=𝑡𝑢𝑧+𝑧𝑢𝑡	𝜙^(6)=12𝑢𝑢𝑧−12𝑧𝑢^2𝑡+12𝑡𝑢𝑢𝑡𝑧−12𝑡𝑢𝑡𝑢𝑧+12𝑧𝑢𝑢𝑧𝑧+12𝑧𝑢𝑢𝑥𝑥+𝜆^2𝑧−𝜆^2𝑧cosh𝑢
	𝜓^(6)1=−2𝑧𝑢𝑢𝑡𝑥+12𝑧𝑢𝑡𝑢𝑥−12𝑡𝑢𝑢𝑥𝑧+12𝑡𝑢𝑥𝑢𝑧
	𝜋^(6)1=−2𝑡𝑢𝑢𝑡𝑡+𝜆^2𝑡−𝑡𝜆^21cosh𝑢−2𝑢𝑢𝑡+12𝑡𝑢^2𝑧−12𝑧𝑢𝑢𝑡𝑧+12𝑧𝑢𝑧𝑢𝑡+12𝑡𝑢𝑢𝑥𝑥