g=1
T=1
rho=1
sigma[H_]=(1/3)*H^3-((T*H)/(rho*g))
chi[x_,t_,H_,a_]=x-(Sqrt[g*H]-Sqrt[(g/H)*a])*t

h[sigma[H_],chi[x_,t_,H_,a_],b_]=b*Sech[Sqrt[b/(4*sigma[H])]*chi[x,t,H,a]]^2

Manipulate[Plot[((Sech[(1/2)  (-(+(Sqrt[H])) t+x)])^2),{x,0,10},PlotRange->All],{t,0,10},{H,0.1,1}]